Longitudinal differential interferometric confocal microscopy

ABSTRACT

A differential interferometric confocal microscope for measuring an object, the microscope including a source-side pinhole array; a detector-side pinhole array; and an interferometer that images the array of pinholes of the source-side pinhole array onto a first array of spots located in front of an object plane located near where the object is positioned and onto a second array of spots behind the object plane, wherein the first and second arrays of spots are displaced from each other in both a direction normal to the object plane and a direction parallel to the object plane, the interferometer also imaging the first arrays of spots onto a first image plane that is behind the detector-side pinhole array and imaging the second array of spots onto a second image plane that is in front of the detector-side pinhole array wherein each spot of the imaged first array of spots is aligned with a corresponding different spot of the imaged second array of spots and a corresponding different pinhole of the detector-side pinhole array.

[0001] This application claims the benefit of U.S. ProvisionalApplication No. 60/448,360, filed Feb. 19, 2003.

TECHNICAL FIELD

[0002] This invention relates to interferometric, confocal microscopes.

BACKGROUND OF THE INVENTION

[0003] There are a number of different forms of differential confocalmicroscopy. In one differential form, the Nomarski microscope measuresone component of a conjugated quadratures of fields corresponding to theelectrical interference signal of two images superimposed in an imageplane. In another differential form, the conjugated quadratures of adark field are measured one point at a time. In another differentialform, the conjugated quadratures of each of two fields corresponding totwo images are superimposed in an image plane one point at a time. Incommonly owned U.S. Provisional Patent Application No. 60/447,254(ZI-40) entitled “Transverse Differential Interferometric ConfocalMicroscopy” and U.S. patent application Ser. No. ______ filed Feb. 13,2004 (ZI-40) also entitled “Transverse Differential InterferometricConfocal Microscopy” both of which are both by Henry A. Hill, it istaught how to practice transverse differential interferometric confocalmicroscopy. The contents of the cited U.S. Provisional Application andthe U.S. Patent Application are herein incorporated in their entirety byreference.

[0004] However, neither the prior art nor the cited U.S. provisionalpatent application and cited U.S. Patent Application teach how topractice differential interferometric confocal microscopy wherein anarray of conjugated quadratures of fields are measured jointly, wherethe components of each conjugated quadratures may be measured jointly,and where each conjugated quadratures represent a difference ofconjugated quadratures of fields of converging beams subsequentlyscattered/reflected from a pair of locations on a substrate surfacewherein one of the converging beams subsequently scattered/reflected ortransmitted by the pair of locations is focused to an image planelocated above the substrate surface and the second of the convergingbeams subsequently scattered/reflected from the pair of locations isfocused to an image plane located below the substrate surface.

[0005] Also, prior art does not teach how to practice dark fielddifferential interferometric confocal microscopy wherein an array ofconjugated quadratures of fields are measured jointly, where thecomponents of each conjugated quadratures may be measured jointly, whereeach conjugated quadratures represents a difference of conjugatedquadratures of fields of converging beams subsequentlyscattered/reflected or transmitted by a pair of locations on a substratesurface wherein one of the converging beams subsequentlyscattered/reflected from the pair of locations is focused to an imageplane located above the substrate surface and the second of theconverging beams subsequently scattered/reflected or transmitted by thepair of locations is focused to an image plane located below thesubstrate surface, and where the nominal values of the conjugatedquadratures of the array of conjugated quadratures is zero, i.e., thefield that is being measured is nominally dark.

SUMMARY OF THE INVENTION

[0006] Embodiments of the present invention comprise interferometricconfocal microscopy systems wherein an array of conjugated quadraturesof fields are measured jointly, where the components of each conjugatedquadratures may be measured jointly, where each conjugated quadraturesrepresents a difference of conjugated quadratures of fields ofconverging beams subsequently scattered/reflected or transmitted by apair of locations on a substrate surface wherein one of the convergingbeams subsequently scattered/reflected or transmitted by the pair oflocations is focused to an image plane located above the substratesurface and the second of the converging beams subsequentlyscattered/reflected from the pair of locations is focused to an imageplane located below the substrate surface, and where the nominal valuesof the conjugated quadratures of the array of conjugated quadratures maybe adjusted as a set to be zero by controlling a single systemparameter.

[0007] In general, in one aspect, the invention features a differentialinterferometric confocal microscope for measuring an object. Themicroscope includes a source-side pinhole array; a detector-side pinholearray; and an interferometer that images the array of pinholes of thesource-side pinhole array onto a first array of spots located in frontof an object plane located near where the object is positioned and ontoa second array of spots behind the object plane, wherein the first andsecond arrays of spots are displaced from each other in both a directionnormal to the object plane and a direction parallel to the object plane.The interferometer also images the first arrays of spots onto a firstimage plane that is behind the detector-side pinhole array and imagesthe second array of spots onto a second image plane that is in front ofthe detector-side pinhole array wherein each spot of the imaged firstarray of spots is aligned with a corresponding different spot of theimaged second array of spots and a corresponding different pinhole ofthe detector-side pinhole array.

[0008] In general, in another aspect, the invention features adifferential interferometric confocal microscope for measuring anobject, wherein the microscope includes a source-side pinhole array; adetector-side pinhole array; and an interferometer that images eachpinhole of the source-side pinhole array onto a corresponding differentpair of two locations, one of which lies in a first object plane and theother of which lies in a second object plane that is parallel to anddisplaced from the first object plane, thereby generating a first imageof the source-side pinhole array in the first object plane and a secondimage of the source-side pinhole array in the second object plane. Theinterferometer also projects a first array of return measurement beamsfrom the first image and a second array of return measurement beams fromthe second image toward the detector-side pinhole array to produce afirst array of converging beams and a second array of converging beams,wherein the detector-side pinhole array generates an array of conjugatedquadratures of fields that is a difference of conjugated quadratures offields of the first and second arrays of converging beams.

[0009] In general, in still another aspect, the invention features adifferential interferometric confocal microscope for measuring an objectand which has, in the vicinity of where the object being measured is tobe located, a first object plane and a second object plane that isdisplaced from and parallel to the first object plane. The microscopeincludes: a source-side pinhole array; a detector-side pinhole array;and an interferometer that receives a beam from a selected pinhole ofthe source-side pinhole array and converges a first part of thatreceived beam onto a corresponding first location in the first objectplane and a second part of that received beam onto a correspondingsecond location in the second object plane. The interferometer isfurther arranged to receive a first return beam from the first locationand a second return beam from the second location and converge at leasta part of each of the first and second return beams onto a correspondingpinhole of the detector-side pinhole array to produce a difference ofconjugated quadratures of fields of the first and second return beamsconverging on that corresponding pinhole, wherein the selected pinholeis any pinhole of the source-side pinhole array.

[0010] In general, in still yet another aspect, the invention features adifferential interferometric confocal microscope for measuring anobject. The microscope includes: a source-side pinhole array forproducing an array of input beams; a detector-side pinhole array; and aninterferometer. The interferometer includes a first optical elementproviding a first reflecting surface; a second optical element providinga second reflecting surface; and a beam splitter positioned between thefirst and second optical elements, wherein the beam splitter producesfrom the array of input beams a first array of measurement beams and asecond array of measurement beams, wherein the first reflecting surfaceparticipates in focusing the first array of measurement beams onto afirst array of locations on a first object plane in object space and thesecond reflecting surface participates in focusing the second array ofmeasurement beams onto a second array of locations on a second objectplane in object space, the first and second object planes being parallelto and displaced from each other. Also, the first array of measurementbeams generates a first array of return beams from the object and thesecond array of measurement beams generates a second array of returnbeams from the object, and the first reflecting element participates inproducing from the first array of return beams a first array ofconverging beams that converge to a first array of spots on a firstimage plane and the second reflecting element participates in producingfrom the second array of return beams a second array of converging beamsthat converge onto a second array of spots on a second image plane. Thefirst and second image planes are adjacent to and on opposite sides ofthe detector-side pinhole array, and wherein the detector-side pinholearray combines the first and second arrays of converging beams to forman array of output beams.

[0011] Other embodiments include one or more of the following features.A single pinhole array serves as both the source-side pinhole array andthe detector-side pinhole array. The first optical element is locatedbetween the single pinhole array and the beam splitter and wherein thesecond optical element is located between a location at which the objectis positioned during use and the beam splitter. The the first reflectingsurface has a center of curvature for which there is a correspondingconjugate as viewed through the beam splitter, and the second reflectingsurface has a center of curvature that is displaced relative to thecorresponding conjugate of the center of curvature of the firstreflecting surface. More specifically, the conjugate of the center ofcurvature of the first reflecting surface and the center of curvature ofthe second reflecting surface are displaced from each other in a firstdirection that is normal to a plane defined by the beam splitter and ina second direction that is parallel to the plane defined by the beamsplitter. The reflecting surface participates in focusing the firstarray of measurement beams via the beam splitter onto the first array oflocations and the second reflecting surface participates in focusing thesecond array of measurement beams via the beam splitter onto the secondarray of locations. The first reflecting element participates incombination with the beam splitter in producing the first array ofconverging beams and the second reflecting element participates incombination with the beam splitter in producing the second array ofconverging beams. The first reflecting surface is substantiallyconcentric with a point on the object. The second optical elementprovides a refracting surface positioned between the object and the beamsplitter to receive light rays from the object. The first reflectingsurface substantially conforms to a sphere having a first radius and therefracting surface conforms to a sphere having a second radius, whereinthe first radius is greater than the second radius. The first opticalelement provides a refracting surface positioned between the beamsplitter and the single pinhole array. The second reflecting surface issubstantially concentric with an image point on the single pinholearray. The second reflecting surface substantially conforms to a spherehaving a first radius and the refracting surface conforms to a spherehaving a second radius, wherein the first radius is greater than thesecond radius. The single pinhole array is a two-dimensional array; morespecifically, a two-dimensional array of equally-spaced holes, which arecircular apertures. The first and second object planes are separatedfrom each other on the order of the longitudinal resolution of thedifferential confocal interferometric microscope.

[0012] An advantage of at least one embodiment of the present inventionis that the fields of beams scattered/reflected or transmitted by a pairof locations on a substrate surface are generated by a single confocalpinhole.

[0013] Another advantage of at least one embodiment of the presentinvention is that reference beam components of an array of referencebeams used in generation of electrical interference signalscorresponding to measured conjugated quadratures of fields of beamsscattered/reflected or transmitted by a pair of locations on a substrateare identical.

[0014] Another advantage of at least one embodiment of the presentinvention is that components of background beams generated bymeasurement beam components subsequently scattered/reflected ortransmitted at a pair of locations on a substrate surface aresubstantially identical at a confocal pinhole.

[0015] Another advantage of at least one embodiment of the presentinvention is that the spatial filtering of fields of beamsscattered/reflected or transmitted at a pair of locations on a substratesurface is performed by a single confocal pinhole.

[0016] Another advantage of at least one embodiment of the presentinvention is that information about a substrate surface is obtained withan interferometric confocal imaging system operating in a dark fieldmode.

[0017] Another advantage of at least one embodiment of the presentinvention is that information about a substrate surface is obtained withreduced systematic and statistical errors.

[0018] Another advantage of at least one embodiment of the presentinvention is the generation of a significant increase in throughputbecause the intensity of an input beam may be significantly increasedwithout saturation of a detector system.

[0019] Another advantage of at least one embodiment of the presentinvention is that an array of conjugated quadratures of the fields ofbeams scattered/reflected or transmitted by a pair of locations on asubstrate surface is measured jointly and the components of eachconjugated quadratures may be measured jointly.

[0020] Another advantage of at least one embodiment of the presentinvention is that information is obtained about critical dimensions andlocations of sub-wavelength artifacts on a substrate surface.

[0021] Another advantage of at least one embodiment of the presentinvention is that information is obtained about the sizes and locationsof sub-wavelength defects on a substrate surface.

[0022] Another advantage of at least one embodiment of the presentinvention is that information may be obtained about a longitudinalderivative of a profile of a substrate surface.

[0023] Another advantage of at least one embodiment of the presentinvention is that information may be obtained about one-dimensional andtwo-dimensional profiles of a substrate surface.

[0024] Another advantage of at least one embodiment of the presentinvention is that imaging of a longitudinal gradient of a substratesurface profile with a lateral resolution of the order of 100 nm and alongitudinal resolution of the order of 200 nm may be obtained with aworking distance of the order of a mm.

[0025] The details of one or more embodiments of the invention are setforth in the accompanying drawings and the description below. Otherfeatures, objects, and advantages of the invention will be apparent fromthe description and drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0026]FIG. 1a is a diagram of an interferometric system used to makedifferential measurements of conjugated quadratures of fields of beamsscattered/reflected or transmitted by a substrate.

[0027]FIG. 1b is a schematic diagram of a beam-conditioner configured tooperate in a two-frequency generator and phase-shifter.

[0028]FIG. 1c is a schematic diagram of a beam-conditioner configured tooperate in a two-frequency generator and frequency-shifter.

[0029]FIG. 2a is a schematic diagram of a confocal microscope system.

[0030]FIG. 2b is a schematic diagram of catadioptric imaging system.

[0031]FIG. 2c is a schematic diagram of beams focused to spots at apinhole array used in a confocal microscope system.

[0032]FIG. 2d is a schematic diagram of beams focused to spots in acatadioptric imaging system.

[0033]FIG. 2e is a schematic diagram of beams focused to spots in acatadioptric imaging system.

[0034]FIG. 2f is a schematic diagram of beams focused to spots in animage plane.

[0035]FIG. 3 is a schematic diagram of an interferometric confocalimaging system used to make differential measurements of conjugatedquadratures of fields of beams scattered/reflected by a substrate.

DETAILED DESCRIPTION

[0036] In general, an array of conjugated quadratures of fields ismeasured interferometrically by a differential confocal interferometerand detector system wherein each conjugated quadratures comprises adifference of conjugated quadratures of fields of converging beamsscattered/reflected or transmitted by a pair of locations on a substratesurface. One of the converging beams subsequently scattered/reflectedfrom the pair of locations is converging to a spot in a first imageplane located above the substrate surface and the other of theconverging beams subsequently scattered/reflected from the pair oflocations is converging to a spot in a second image plane located belowthe substrate surface. The array of conjugated quadratures is measuredjointly, i.e., simultaneously, and the components of each conjugatedquadratures may be measured jointly. The separation of the first andsecond image planes is of the order of the longitudinal resolution ofthe differential confocal interferometer and detector system. Each pairof locations generally has a relative displacement of the order of thetransverse resolution of the differential confocal interferometer anddetector system in a direction nominally tangent to the substratesurface. The relative phases of the converging beams subsequentlyscattered/reflected by the substrate surface may be adjusted as a set bycontrol of a single system parameter so that the conjugated quadraturesof the array of conjugated quadratures are nominally zero, i.e.,information may be obtained about the substrate surface with theinterferometer and detector system operating in a dark field mode.Operation in a dark field mode leads to both reduced systematic andstatistical errors in the information and to increased throughput. Theinformation may comprise one-dimensional and two-dimensionallongitudinal profiles of a substrate surface, one-dimensional andtwo-dimensional longitudinal derivatives of a profile of a substratesurface; critical dimensions of features or artifacts on a substratesurface; and the size and location of sub-wavelength defects on asubstrate surface.

[0037] In one embodiment, an image plane of an interferometric confocalimaging system comprises a superposition of two images of a substratesurface wherein each of the two superimposed images corresponds to apartially defocused image of a location on the substrate surface and thetwo partially defocused images are displaced transversely relative toeach other. An array of conjugated quadratures of fields representingthe superimposed images are measured jointly and the components of eachconjugated quadratures may be measured jointly. Each pair of locationson the substrate surface corresponding to a conjugated quadratures ofthe array of conjugated quadratures generally has a relative transversedisplacement of the order of 3 times the size of the transverseresolution of the interferometric confocal imaging system in a directionnominally tangent to the surface of the imaged section. The longitudinalseparation of the image planes of the beams generating the partiallydefocused images of the substrate surface is of the order of thelongitudinal resolution of the interferometric confocal imaging system.The respective conjugated quadrature of a field is a sin φ when thequadrature x(φ) of the field is a cos φ.

[0038] In another embodiment, the relative phases of beams subsequentlyscattered/reflected or transmitted at a pair of locations on a substratesurface may be adjusted by a single confocal imaging system parameter sothat conjugated quadratures of an array of conjugated quadratures offields of the scattered/reflected or transmitted beams from therespective pair of locations are nominally zero, i.e., information isobtained about the substrate surface with the interferometric imagingsystem operating in a dark field mode.

[0039] Operation in a dark field mode leads to both reduced systematicand statistical errors in the information. When operating in a darkfield mode, a measured conjugated quadratures of fields of beamsscattered/reflected or transmitted from a respective pair of locationscomprising a sub-wavelength artifact in an otherwise locally isotropicsubstrate surface represents information only about the sub-wavelengthartifact relative to a reference sub-wavelength artifact. The referenceartifact has properties of the otherwise locally isotropic substratesurface and dimensions similar to those of the artifact. Accordingly,properties measured include information about critical dimensions andlocation of the sub-wavelength artifact on the substrate.

[0040] Also when operating in the dark field mode, a measured conjugatedquadratures of fields of beams scattered/reflected or transmitted by arespective pair of locations on a substrate surface comprising asub-wavelength defect in an otherwise locally isotropic substratesurface represents information only about the sub-wavelength defectrelative to a reference sub-wavelength defect. The reference defect hasproperties of the otherwise locally isotropic substrate surface anddimensions similar to those of the defect. Accordingly, propertiesmeasured include information about dimensions and location of thesub-wavelength defect on the substrate.

[0041] A general description of embodiments incorporating aspects of thepresent invention will first be given wherein the embodiments comprisean interferometer system that uses either a single-, double, bi-, orquad-homodyne detection method and a partially defocused image of anarray of a first a set of locations on a substrate surface and apartially defocused image of an array of a second set of locations onthe substrate surface are superimposed on an image plane of theinterferometer system. The transverse spacing between pairs of locationscomprising corresponding locations of the first and second sets oflocations on the substrate surface is of the order of at least 3 timesthe size of the transverse resolution of the interferometer system. Thelongitudinal separation of the image planes of the beams generating thepartially defocused images of the substrate surface is of the order ofthe longitudinal resolution of the interferometer system. There is aone-to-two mapping of a location in the superimposed image space to thetwo locations of pair of locations.

[0042] Referring to FIG. 1a, an interferometer system is showndiagrammatically comprising an interferometer generally shown as numeral10, a source 18, a beam-conditioner 22, detector 70, an electronicprocessor and controller 80, and a measurement object or substrate 60.Source 18 and beam conditioner 22 generate input beam 24 comprising oneor more frequency components. Source 18 is a pulsed source. Two or moreof the frequency components of input beam 24 may be coextensive in spaceand may have the same temporal window function.

[0043] Reference and measurement beams are generated in interferometer10 for each of the frequency components of beam 24. The measurement beamgenerated in interferometer 10 is one component of beam 28 and imaged toform a partially defocused image on the surface of substrate 60 to forman array of pairs of partially defocused images. Beam 28 furthercomprises a return reflected/scattered measurement beam that isgenerated by the reflection/scattering or transmission of themeasurement beam component of beam 28 at the array of pairs of partiallydefocused images on the surface of substrate 60. Interferometer 10superimposes the two arrays of components of the return measurement beamcorresponding to the two arrays components of beam 28reflected/scattered or transmitted at the arrays of the pairs ofdefocused images to form a single array of superimposed images of returnmeasurement beam components of beam 28. The return measurement beamcomponents of beam 28 are subsequently combined with the reference beamin interferometer 10 to form output beam 32.

[0044] Output beam 32 is detected by detector 70 to generate anelectrical interference signal 72. Detector 70 may comprise an analyzerto select common polarization states of the reference and returnmeasurement beam components of beam 32 to form a mixed beam.Alternatively, interferometer 10 may comprise an analyzer to selectcommon polarization states of the reference and return measurement beamcomponents such that beam 32 is a mixed beam.

[0045] Two different modes are described for the acquisition of theelectrical interference signals 72. The first mode to be described is astep and stare mode wherein substrate 60 is stepped between fixedlocations corresponding to locations where image information is desired.The second mode is a scanning mode. In the step and stare mode forgenerating a one-dimensional and a two-dimensional surface profile ofsubstrate 60, substrate 60 mounted in wafer chuck 84/stage 90 istranslated by stage 90. The position of stage 90 is controlled bytransducer 82 according to servo control signal 78 from electronicprocessor and controller 80. The position of stage 90 is measured bymetrology system 88 and position information acquired by metrologysystem 88 is transmitted to electronic processor and controller 80 togenerate an error signal for use in the position control of stage 90.Metrology system 88 may comprise for example linear displacement andangular displacement interferometers and cap gauges.

[0046] Electronic processor and controller 80 translates wafer stage 90to a desired position and then acquires a set of four electricalinterference signal values. After the acquisition of the sequence offour electrical interference signals, electronic processor andcontroller 80 then repeats the procedure for the next desired positionof stage 90. The elevation and angular orientation of substrate 60 iscontrolled by transducers 86A and 86B.

[0047] The second mode for the acquisition of the electricalinterference signal values is next described wherein the electricalinterference signal values are obtained with the position of stage 90scanned in one or more directions. In the scanning mode, source 18 ispulsed at times controlled by signal 92 from signal processor andcontroller 80. Source 18 is pulsed at times corresponding to theregistration of the conjugate image of confocal pinholes or pixels ofdetector 70 with positions on and/or in substrate 60 for which imageinformation is desired.

[0048] There will be a restriction on the duration or “pulse width” of abeam pulse τ_(p1) produced by source 18 as a result of the continuousscanning mode used in the third variant of the first embodiment. Pulsewidth τ_(p1) will be a parameter that in part controls the limitingvalue for spatial resolution in the direction of a scan to a lower boundof

τ_(p1)V,  (1)

[0049] where V is the scan speed. For example, with a value of τ_(p1)=50nsec and a scan speed of V=0.20 m/sec, the limiting value of the spatialresolution τ_(p1)V in the direction of scan will be

τ_(p1)V=10 nm.  (2)

[0050] Pulse width τ_(p1) will also determine the minimum frequencydifference that can be used in the bi- and quad-homodyne detectionmethods. In order that there be no contributions to the electricalinterference signals from interference between fields of conjugatedquadratures, the minimum frequency spacing Δf_(min) is expressed as$\begin{matrix}{{\Delta \quad f_{\min}}\operatorname{>>}{\frac{1}{\tau_{p1}}.}} & (3)\end{matrix}$

[0051] For an example of τ_(p1)=50 nsec, 1/τ_(p1)=20 MHz.

[0052] For certain embodiments, the frequencies of input beam 24 arecontrolled by signals 74 and/or 92 from signal processor and controller80 to correspond to the frequencies that will yield the desired phaseshifts between the reference and return measurement beam components ofoutput beam 32. Alternatively in certain other embodiments, the relativephases of reference and measurement beam components of input beam 24 arecontrolled by signal 74 and/or 92 from signal processor and controller80 to correspond to the desired phase shifts between the reference andreturn measurement beam components of output beam 32. In the first mode,i.e., the step and stare mode, each set of the sets of arrays of fourelectrical interference signal values corresponding to the set of fourphase shift values are generated by a single pixel of detector 70 forsingle- and bi-homodyne detection method, by two pixels of detector 70for the quad-homodyne detection method, and by four pixels of detector70 for the double-homodyne detection methods. In the second mode for theacquisition of the electrical interference signal values, eachcorresponding set of four electrical interference signal values aregenerated by a conjugate set of four different pixels of detector 70 foreach of the four homodyne detection methods. Thus in the first mode ofacquisition, the differences in pixel efficiency are compensated in thesignal processing by signal processor and controller 80 for the double-,bi-, and quad-homodyne detection methods and in the second mode ofacquisition, the differences in pixel efficiency and the differences insizes of pinholes in confocal pinhole arrays are compensated in thesignal processing by signal processor and controller 80 as described inthe subsequent description of the homodyne detection methods. The jointmeasurements of conjugated quadratures of fields generated by electricprocessor and controller 80 are subsequently described in thedescription of the bi- and quad-homodyne detection methods.

[0053] In practice, known phase shifts are introduced between thereference and measurement beam components of output beam 32 by twodifferent techniques. In one technique, phase shifts are introducedbetween the reference and measurement beam components for each of the atleast two frequency components by source 18 and beam-conditioner 22 ascontrolled by signals 92 and 74, respectively, from electronic processorand controller 80. In the second technique, phase shifts are introducedbetween the reference and measurement beam components for each of the atleast two frequency components as a consequence of frequency shiftsintroduced to the frequency components of input beam 24 by source 18 andbeam-conditioner 22 as controlled by signals 92 and 74, respectively,from electronic processor and controller 80.

[0054] There are different ways to configure source 18 andbeam-conditioner 22 to meet the input beam requirements of differentembodiments. Reference is made to FIG. 1b where beam-conditioner 22 isconfigured as a two-frequency generator and a phase-shifter and source18 is configured to generate beam 20 with one frequency component. Thetwo-frequency generator and phase-shifter configuration comprisesacousto-optic modulators 1020, 1026, 1064, and 1068; polarizingbeam-splitters 1030, 1042, 1044, and 1056; phase-shifters 1040 and 1052;half wave phase retardation plates 1072 and 1074; non-polarizingbeam-splitter 1070, and mirrors 1036, 1038, 1050, 1054, and 1056.

[0055] Input beam 20 is incident on acousto-optic modulator 1020 with aplane of polarization parallel to the plane of FIG. 1b. A first portionof beam 20 is diffracted by acousto-optic modulator 1020 as beam 1022and then by acousto-optic modulator 1026 as beam 1028 having apolarization parallel to the plane of FIG. 1b. A second portion of beam20 is transmitted as a non-diffracted beam 1024 having a plane ofpolarization parallel to the plane of FIG. 1b. The acoustic power toacousto-optic modulator 1020 is adjusted such that beams 1022 and 1024have nominally the same intensity.

[0056] Acousto-optic modulators 1020 and 1026 may be of either thenon-isotropic Bragg diffraction type or of the isotropic Braggdiffraction type. The frequency shifts introduced by acousto-opticmodulators 1020 and 1026 are of the same sign and equal to ¼ of thedesired frequency shift between the two frequency components of inputbeam 24. Also the direction of propagation of beam 1028 is parallel tothe direction of propagation of beam 1024.

[0057] Beam 1024 is diffracted by acousto-optic modulators 1064 and 1068as beam 1082 having a polarization parallel to the plane of FIG. 1b.Acousto-optic modulators 1064 and 1068 may be of either thenon-isotropic Bragg diffraction type or of the isotropic Braggdiffraction type. The frequency shifts introduced by acousto-opticmodulators 1064 and 1068 are of the same sign and equal to ¼ of thedesired frequency shift between the two frequency components of inputbeam 24. Also the direction of propagation of beam 1082 is parallel tothe direction of propagation of beam 1024.

[0058] Beams 1028 and 1082 are incident on half-wave phase retardationplates 1072 and 1074, respectively, and transmitted as beams 1076 and1078, respectively. Half-wave phase retardation plates 1072 and 1074 areoriented such that the planes of polarization of beams 1076 and 1078 areat 45 degrees to the plane of FIG. 1b. The components of beams 1076 and1078 polarized parallel to the plane of FIG. 1b will be used as themeasurement beam components in interferometer 10 and the components ofbeams 1076 and 1078 polarized orthogonal to the plane of FIG. 1b will beused as the reference beam components in interferometer 10.

[0059] Continuing with reference to FIG. 1b, beam 1076 is incident onpolarizing beam-splitter 1044 and the respective measurement andreference beam components transmitted and reflected, respectively, asbeams 1046 and 1048, respectively. Measurement beam component 1046 istransmitted by polarizing beam-splitter 1056 as a measurement beamcomponent of beam 1058 after reflection by mirror 1054. Reference beamcomponent 1048 is reflected by polarizing beam-splitter 1056 asreference beam component of beam 1058 after reflection by mirror 1050and transmission by phase-shifter 1052. Beam 1058 is incident onbeam-splitter 1070 and a portion thereof is reflected as a component ofbeam 24.

[0060] Beam 1078 is incident on polarizing beam-splitter 1030 and therespective measurement and reference beam components transmitted andreflected, respectively, as beams 1032 and 1034, respectively.Measurement beam component 1032 is transmitted by polarizingbeam-splitter 1042 as a measurement beam component of beam 1060 afterreflection by mirror 1036. Reference beam component 1034 is reflected bypolarizing beam splitter 1042 as reference beam component of beam 1060after reflection by mirror 1038 and transmission by phase-shifter 1040.Beam 1060 is incident on beam-splitter 1070 and a portion thereof istransmitted as a component of beam 24 after reflection by mirror 1056.

[0061] Phase-shifters 1052 and 1040 introduce phase shifts betweenrespective reference and measurement beams according to signal 74 fromelectronic processor and controller 80 (see FIG. 1a). The schedule ofthe respective phase shifts is described in the subsequent discussionsof homodyne detection methods. Phase-shifters 1052 and 1040 may be forexample of the optical-mechanical type comprising for example prisms andpiezoelectric translators or of the electro-optical modulator type.

[0062] Beam 24 that exits the two-frequency generator and phase shiftconfiguration of beam-conditioner 22 comprises one reference beam andmeasurement beam having one frequency, a second reference beam andmeasurement beam having a second frequency component, and relativephases of the reference beams and the measurement beams that arecontrolled by electronic processor and controller 80.

[0063] Continuing with a description of different ways to configuresource 18 and beam-conditioner 22 to meet the input beam requirements ofdifferent embodiments, reference is made to FIG. 1c wherebeam-conditioner 22 is configured as a two-frequency generator and afrequency shifter. The two-frequency generator and frequency-shifterconfiguration comprises acousto-optic modulators 1120, 1126, 1130, 1132,1142, 1146, 1150, 1154, 1058, and 1062; beam-splitter 1168; and mirror1166.

[0064] Source 18 is configured to generate beam 20 with a singlefrequency component. Beam 20 is incident on acousto-optic modulator 1120with a plane of polarization parallel to the plane of FIG. 1c. A firstportion of beam 20 is diffracted by acousto-optic modulator 1120 as beam1122 and then by acousto-optic modulator 1126 as beam 1128 having apolarization parallel to the plane of FIG. 1c. A second portion of beam20 is transmitted as a non-diffracted beam 1124 having a plane ofpolarization parallel to the plane of FIG. 1c. The acoustic power toacousto-optic modulator 1120 is adjusted such that beams 1122 and 1124have nominally the same intensity.

[0065] Acousto-optic modulators 1120 and 1126 may be of either thenon-isotropic Bragg diffraction type or of the isotropic Braggdiffraction type. The frequency shifts introduced by acousto-opticmodulators 1120 and 1126 are of the same sign and equal to ½ of afrequency shift Δf that will generate in interferometer 10 a relativeπ/2 phase shift between a corresponding reference beam and a measurementbeam that have a relative change in frequency equal to the frequencyshift. The direction of propagation of beam 1128 is parallel to thedirection of propagation of beam 1124.

[0066] Continuing with FIG. 1c, beam 1128 is incident on acousto-opticmodulator 1132 and is either diffracted by acousto-optic modulator 1132as beam 1134 or transmitted by acousto-optic modulator 1132 as beam 1136according to control signal 74 (see FIG. 1a) from electronic processorand controller 80. When beam 1134 is generated, beam 1134 is diffractedby acousto-optic modulators 1142, 1146, and 1150 as a frequency-shiftedbeam component of beam 1152. The frequency shifts introduced byacousto-optic modulators 1132, 1142, 1146, and 1150 are all in the samedirection and equal in magnitude to Δf/2. Thus the net frequency shiftintroduced by acousto-optic modulators 1132, 1142, 1146, and 1150 is±2Δf and will generate a relative π phase between the respectivereference and measurement beams in interferometer 10. The net frequencyshift introduced by acousto-optic modulators 1120, 1126, 1132, 1142,1146, and 1150 is Δf±2Δf and will generate a respective relative phaseshift of π/2±π between the respective reference and measurement beams ininterferometer 10.

[0067] When beam 1136 is generated, beam 1136 is transmitted byacousto-optic modulator 1150 according to control signal 74 fromelectronic processor and controller 80 as a non-frequency shifted beamcomponent of beam 1152 with respect to beam 1128. The frequency shiftintroduced by acousto-optic modulators 1120, 1126, and 1150 is Δf andwill generate a respective relative phase shift of π/2 between therespective reference and measurement beams in interferometer 10.

[0068] Beam 1124 is incident on acousto-optic modulator 1130 and iseither diffracted by acousto-optic modulator 1130 as beam 1140 ortransmitted by acousto-optic modulator 1130 as beam 1138 according tocontrol signal 74 from electronic processor and controller 80. When beam1140 is generated, beam 1140 is diffracted by acousto-optic modulators1154, 1158, and 1162 as a frequency-shifted beam component of beam 1164.The frequency shifts introduced by acousto-optic modulators 1130, 1154,1158, and 1162 are all in the same direction and equal to ±Δf/2. Thusthe net frequency shift introduced by acousto-optic modulators 1130,1154, 1158, and 1162 is ±Δf/2 and will generate a relative phase shiftof π between the respective reference and measurement beams on transitthrough interferometer 10. The net frequency shift introduced byacousto-optic modulators 1120, 1130, 1154, 1158, and 1162 is ±Δf/2 andwill generate a respective relative phase shift of ±π between therespective reference and measurement beams on transit throughinterferometer 10

[0069] When beam 1138 is generated, beam 1138 is transmitted byacousto-optic modulator 1162 according to control signal 74 fromelectronic processor and controller 80 as a non-frequency shifted beamcomponent of beam 1164. The frequency shift introduced by acousto-opticmodulators 1120, 1130, and 1162 is 0 and will generate a respectiverelative phase shift of 0 between the respective reference andmeasurement beams on transit through interferometer 10.

[0070] Beams 1152 and 1164 may be used directly as input beam 24 when anembodiment requires spatially separated reference and measurement beamsfor an input beam. When an embodiment requires coextensive reference andmeasurement beams as an input beam, beam 1152 and 1164 are next combinedby beam-splitter 1168 to form beam 24. Acousto-optic modulators 1120,1126, 1130, 1132, 1142, 1146, 1150, 1154, 1058, and 1062 may be eitherof the non-isotropic Bragg diffraction type or of the isotropic Braggdiffraction type. Beams 1152 and 1164 are both polarized in the plane ofFIG. 1c for either non-isotropic Bragg diffraction type or of theisotropic Bragg diffraction type and beam-splitter 1168 is of thenon-polarizing type.

[0071] With a continuation of the description of different ways toconfigure source 18 and beam-conditioner 22 to meet the input beamrequirements of different embodiments, source 18 will preferablycomprise a pulsed source. There are a number of different ways forproducing a pulsed source [see Chapter 11 entitled “Lasers”, Handbook ofOptics, 1, 1995 (McGraw-Hill, New York) by W. Silfvast]. Each pulse ofsource 18 may comprise a single pulse or a train of pulses such asgenerated by a mode locked Q-switched Nd:YAG laser. A single pulse trainis referenced herein as a pulse sequence and a pulse and a pulsesequence are used herein interchangeably.

[0072] Source 18 may be configured in certain embodiments to generateone or more frequencies by techniques such as described in a reviewarticle entitled “Tunable, Coherent Sources For High-Resolution VUV andXUV Spectroscopy” by B. P. Stoicheff, J. R. Banic, P. Herman, W. Jamroz,P. E. LaRocque, and R. H. Lipson in Laser Techniques for ExtremeUltraviolet Spectroscopy, T. J. McIlrath and R. R. Freeman, Eds.,(American Institute of Physics) p 19 (1982) and references therein. Thetechniques include for example second and third harmonic generation andparametric generation such as described in the articles entitled“Generation of Ultraviolet and Vacuum Ultraviolet Radiation” by S. E.Harris, J. F. Young, A. H. Kung, D. M. Bloom, and G. C. Bjorklund inLaser Spectroscopy I, R. G. Brewer and A. Mooradi, Eds. (Plenum Press,New York) p 59, (1974) and “Generation of Tunable Picosecond VUVRadiation” by A. H. Kung, Appl. Phys. Lett. 25, p 653 (1974). Thecontents of the three cited articles are herein incorporated in theirentirety by reference.

[0073] The output beams from source 18 comprising two or four frequencycomponents may be combined in beam-conditioner 22 by beam-splitters toform coextensive measurement and reference beams that are eitherspatially separated or coextensive as required in various embodiments.When source 18 is configured to furnish two or four frequencycomponents, the frequency shifting of the various components required incertain embodiments may be introduced in source 18 for example byfrequency modulation of input beams to parametric generators and thephase shifting of reference beams relative to measurement beams inbeam-conditioner 22 may be achieved by phase shifters of theoptical-mechanical type comprising for example prisms or mirrors andpiezoelectric translators or of the electro-optical modulator type.

[0074] The general description of embodiments incorporating variousaspects of the present invention is continued with reference to FIG. 1a.Input beam 24 is incident on interferometer 10 wherein reference beamsand measurement beams are present in input beam 24 or are generated frominput beam 24 in interferometer 10. The reference beams and measurementbeams comprise two arrays of reference beams and two arrays ofmeasurement beams wherein the arrays may comprise arrays of one element.The arrays of measurement beams are incident on or focused on and/or insubstrate 60 and arrays of return measurement beams are generated byreflection/scattering and/or transmission by the substrate. In the caseof single element arrays for the reference beams and measurement beams,the measurement beams are generally reflected or transmitted bysubstrate 60. The arrays of reference beams and return measurement beamsare combined by a beam-splitter to form two arrays of output beamcomponents. The arrays of output beam components are mixed with respectto state of polarization either in interferometer 10 or in detector 70.The arrays of output beams are subsequently focused to spots on pixelsof a multi-pixel or single pixel detector as required and detected togenerate electrical interference signal 72.

[0075] There are four different implementations of the homodynedetection method that are used in interferometric embodiments. The fourdifferent implementations are referred to as single-, double-, bi-, andquad-homodyne detection methods. For the single-homodyne detectionmethod, input beam 24 comprises a single frequency component and a setof four measurements of the array of electrical interference signals 72is made. For each of the four measurements of the array of electricalinterference signals 72, a known phase shift is introduced between thereference beam component and respective return measurement beamcomponents of output beam 32. The subsequent data processing procedureused to extract the conjugated quadratures of the reflected and/orscattered or transmitted return measurement beam for an input beamcomprising a single frequency component is described for example incommonly owned U.S. Pat. No. 6,445,453 (ZI-14) entitled “ScanningInterferometric Near-Field Confocal Microscopy” by Henry A. Hill, thecontents of which are herein incorporated in their entirety byreference.

[0076] The double-homodyne detection method uses input beam 24comprising four frequency components and four detectors to obtainmeasurements of electrical interference signals that are subsequentlyused to obtain conjugated quadratures. Each detector element of the fourdetector elements obtains a different one of the four electricalinterference signal values with the four electrical interference signalvalues obtained simultaneously to compute the conjugated quadratures fora field. Each of the four electrical interference signal values containsonly information relevant to one orthogonal component of the conjugatedquadratures. The double-homodyne detection used herein is related to thedetection methods such as described in Section IV of the article by G. MD'ariano and M G. A. Paris entitled. “Lower Bounds On Phase SensitivityIn Ideal And Feasible Measurements,” Phys. Rev. A 49, 3022-3036 (1994).Accordingly, the double-homodyne detection method does not make jointdeterminations of conjugated quadratures of fields wherein eachelectrical interference signal value contains information simultaneouslyabout each of two orthogonal components of the conjugated quadratures.

[0077] The bi- and quad-homodyne detection methods obtain measurementsof electrical interference signals wherein each measured value of anelectrical interference signal contains simultaneously information abouttwo orthogonal components of conjugated quadratures. The two orthogonalcomponents correspond to orthogonal components of conjugated quadraturessuch as described in cited U.S Provisional Patent Application No.60/442,858 (ZI-47) and cited U.S. Patent Application filed Jan. 27, 2004(ZI-47) entitled “Apparatus and Method for Joint Measurements ofConjugated Quadratures of Fields of Reflected/Scattered and TransmittedBeams by an Object in Interferometry.”

[0078] Conjugated quadratures of fields of the return measurement beamare obtained by single-, double-, bi-, and quad- homodyne detectionmethods in the interferometric embodiments. For each of the homodynedetection methods, a set of four measurements of the array of electricalinterference signals 72 is made. For each of the four measurements ofthe array of electrical interference signals 72, a known phase shift isintroduced between the reference beam components and respective returnmeasurement beam components of output beam 32. A nonlimiting example ofa known set of phase shifts comprise 0, π/4, π/2, and 3π/2 radians, mod2π.

[0079] Input beam 24 comprises for interferometric embodiments onefrequency component for the single-homodyne detection method. For thebi-homodyne detection method, input beam 24 comprises two frequencycomponents and for double- and quad-homodyne detection methods, inputbeam 24 comprises four frequency components. The phase shifts aregenerated by either shifting the frequencies of frequency components ofinput beam 24 between known frequency values or by introducing phaseshifts between the reference and measurement beam components of inputbeam 24. In certain of the interferometric embodiments, there is adifference between the optical path lengths of the reference beamcomponents and the respective return beam components of output beamcomponents such for output beam 32 in interferometer 10. As aconsequence, a change in frequency of a frequency component of inputbeam 24 will generate a relative phase shift between the correspondingreference beam components and the respective return beam components ofoutput beam 32.

[0080] For an optical path difference L between the reference beamcomponents and the respective return measurement beam components ofoutput beam 32, there will be for a frequency shift Δf a correspondingphase shift φ where $\begin{matrix}{\phi = {2\quad \pi \quad {L\left( \frac{\Delta \quad f}{c} \right)}}} & (4)\end{matrix}$

[0081] and c is the free space speed of light. Note that L is not aphysical path length difference and depends for example on the averageindex of refraction of the measurement beam and the return measurementbeam paths. For an example of a phase shift φ=π, 3π, 5π, . . . and avalue of L=0.25 m, the corresponding frequency shifts are Δf=600 MHz,1.8 GHz, 3.0 GHz, . . . .

[0082] The frequencies of components of input beam 24 are determined bythe mode of operation of source 18 and of beam-conditioner 22 accordingto control signals 92 and 74, respectively, generated by electronicprocessor and controller 80.

[0083] Referring to the bi-homodyne detection method used in someembodiments, a set of four electrical interference signal values areobtained for each pair of spots in or on substrate 60 being imaged suchas described in commonly owned U.S. Provisional Patent Application No.60/442,858 (ZI-47) and entitled “Apparatus and Method for JointMeasurements of Conjugated Quadratures of Fields of Reflected/ScatteredBeams by an Object in Interferometry” and U.S. Patent Application filedJan. 27, 2004 (ZI-47) and entitled “Apparatus and Method for JointMeasurements of Conjugated Quadratures of Fields of Reflected/Scatteredand Transmitted Beams by an Object in Interferometry” both of which areby Henry A. Hill. The contents of both the cited U.S. Provisional PatentApplication and the U.S. Patent Application are herein incorporated intheir entirety by reference. The set of four electrical interferencesignal values S_(j), j=1,2,3,4 used for obtaining conjugated quadraturesof fields for a single a spot on and/or in a substrate being imaged isrepresented for the bi-homodyne detection within a scale factor by theformula $\begin{matrix}{S_{j} = {P_{j}\begin{Bmatrix}\begin{matrix}\begin{matrix}{{\xi_{j}^{2}{A_{1}}^{2}} + {\zeta_{j}^{2}{B_{1}}^{2}} + {\eta_{j}^{2}{C_{1}}^{2}} + {\zeta_{j}\eta_{j}2{B_{1}}{C_{1}}\cos \quad \phi_{B_{1}C_{1}ɛ_{j}}} +} \\{{\xi_{j}\zeta_{j}2{A_{1}}{B_{1}}\cos \quad \phi_{A_{1}B_{1}ɛ_{j}}} + {ɛ_{j}\xi_{j}\eta_{j}2{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}} +}\end{matrix} \\{{\xi_{j}^{2}{A_{2}}^{2}} + {\zeta_{j}^{2}{B_{2}}^{2}} + {\eta_{j}^{2}{C_{2}}^{2}} + {\zeta_{j}\eta_{j}2{B_{2}}{C_{2}}\cos \quad \phi_{B_{2}C_{2}\gamma_{j}}} +}\end{matrix} \\{{\xi_{j}\zeta_{j}2{A_{2}}{B_{2}}\cos \quad \phi_{A_{2}B_{2}\gamma_{j}}} + {\gamma_{j}\xi_{j}\eta_{j}2{A_{2}}{C_{2}}\cos \quad \phi_{A_{2}C_{2}}}}\end{Bmatrix}}} & (5)\end{matrix}$

[0084] where coefficients A₁ and A₂ represent the amplitudes of thereference beams corresponding to the first and second frequencycomponents of the input beam; coefficients B₁ and B₂ represent theamplitudes of background beams corresponding to reference beams A₁ andA₂, respectively; coefficients C₁ and C₂ represent the amplitudes of thereturn measurement beams corresponding to reference beams A₁ and A₂,respectively; P_(j) represents the integrated intensity of the firstfrequency component of the input beam in pulse j of the pulse sequence;and the values for ε_(j) and γ_(j) are listed in Table 1. The change inthe values of ε_(j) and γ_(j) from 1 to −1 or from −1 to 1 correspond tochanges in relative phases of respective reference and measurementbeams. The coefficients ξ_(j), ζ_(j), and η_(j) represent effects ofvariations in properties of a conjugate set of four pinholes such assize and shape used in the generation of the spot on and/or in substrate60 and the sensitivities of a conjugate set of four detector pixelscorresponding to the spot on and/or in substrate 60 for the referencebeam, the background beam, and the return measurement beam,respectively. TABLE 1 j ε_(j) γ_(j) ε_(j)γ_(j) 1 1 1 1 2 −1 −1 1 3 −1 1−1 4 1 −1 −1

[0085] It is assumed in Equation (5) that the ratio of |A₂|/|A₁| is notdependent on j or on the value of P_(j). In order to simplify therepresentation of S_(j) so as to project the important features withoutdeparting from either the scope or spirit of the present invention, itis also assumed in Equation (5) that the ratio of the amplitudes of thereturn measurement beams corresponding to A₂ and A₁ is not dependent onj or on the value of P_(j). However, the ratio |C₂|/|C₁| will bedifferent from the ratio |A₂|/|A₁| when the ratio of the amplitudes ofthe measurement beam components corresponding to A₂ and A₁ are differentfrom the ratio |A₂|/|A₁|.

[0086] Noting that cos φ_(A) ₂ _(C) ₂ =±sin φ_(A) ₁ _(C) ₁ by thecontrol of the relative phase shifts between corresponding reference andreturn measurement beam components in beam 32, Equation (5) may berewritten as $\begin{matrix}{{S_{j} = {P_{j}\begin{Bmatrix}\begin{matrix}\begin{matrix}{{\xi_{j}^{2}\left( {{A_{1}}^{2} + {A_{2}}^{2}} \right)} + {\zeta_{j}^{2}\left( {{B_{1}}^{2} + {B_{2}}^{2}} \right)} + {\eta_{j}^{2}\left( {{C_{1}}^{2} + {C_{2}}^{2}} \right)} +} \\{{2\xi_{j}{\zeta_{j}\left( {{{A_{1}}{B_{1}}\cos \quad \phi_{A_{1}B_{1}ɛ_{j}}} + {{A_{2}}{B_{2}}\cos \quad \phi_{A_{2}B_{2}\gamma_{j}}}} \right)}} +}\end{matrix} \\{{2\xi_{j}{\eta_{j}\begin{bmatrix}{{ɛ_{j}{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}} +} \\{{\gamma_{j}\left( \frac{A_{2}}{A_{1}} \right)}\left( \frac{C_{2}}{C_{1}} \right){A_{1}}{C_{1}}\sin \quad \phi_{A_{1}C_{1}}}\end{bmatrix}}} +}\end{matrix} \\{2\zeta_{j}{\eta_{j}\left\lbrack {{ɛ_{j}{B_{1}}{C_{1}}\cos \quad \phi_{B_{1}C_{1}ɛ_{j}}} + {\gamma_{j}{B_{2}}{C_{2}}\cos \quad \phi_{B_{2}C_{2}\gamma_{j}}}} \right\rbrack}}\end{Bmatrix}}},} & (6)\end{matrix}$

[0087] where the relationship cos φ_(A) ₂ _(C) ₂ =sin φ_(A) ₁ _(C) ₁ hasbeen used without departing from either the scope or spirit of thepresent invention.

[0088] The change in phase φ_(A) ₁ _(B) ₁ _(ε) _(j) φ_(A) ₂ _(B) ₂ _(γ)_(j) for a change in ε_(j) and the change in phase φ_(A) ₁ _(B) ₁ _(ε)_(j) φ_(A) ₂ _(B) ₂ _(γ) _(j) for a change in γ_(j) may be differentfrom π in embodiments depending on where and how the background beam isgenerated. It may be of value in evaluating the effects of thebackground beams to note that the factor cos φ_(B) ₁ _(C) ₁ _(ε) _(j)may be written as cos [φ_(A) ₁ _(C) ₁ +(φ_(B) ₁ _(C) ₁ _(ε) _(j)−φ_(A) ₁_(C) ₁ )] where the phase difference (φ_(B) ₁ _(C) ₁ _(ε) _(j) −φ_(A) ₁_(C) ₁ ) is the same as the phase φ_(A) ₁ _(B) ₁ _(ε) _(j) , i.e., cosφ_(B) ₁ _(C) ₁ _(ε) _(j) =cos (φ_(A) ₁ _(C) ₁ +φ_(A) ₁ _(B) ₁ _(ε) _(j)).

[0089] It is evident from inspection of Equation (6) that the term inEquation (6) corresponding to the component of conjugated quadratures|C₁| cos φ_(A) ₁ _(C) ₁ is a rectangular function that has a mean valueof zero and is symmetric about j=2.5 since εj is symmetric about j=2.5.In addition the term in Equation (6) corresponding to the component ofconjugated quadratures |C₁| sin φ_(A) ₁ _(C) ₁ in Equation (6) is arectangular function that has a mean value of zero and is antisymmetricabout j=2.5 since γ_(j) is a antisymmetric function about j=2.5. Anotherimportant property by the design of the bi-homodyne detection method isthat the conjugated quadratures |C₁| cos φ_(A) ₁ _(C) ₁ and |C₁| sinφ_(A) ₁ _(C) ₁ terms are orthogonal over the range of j=1,2,3,4 sinceε_(j) and γ_(j) are orthogonal over the range of j=1,2,3,4,${i.e.}\quad,{{\sum\limits_{j = 1}^{4}{ɛ_{j}\gamma_{j}}} = 0.}$

[0090] Information about conjugated quadratures |C₁| cos φ_(A) ₁ _(C) ₁and |C₁| sin φ_(A) ₁ _(C) ₁ is obtained using the symmetric andantisymmetric properties and orthogonality property of the conjugatedquadratures terms in Equation (6) as represented by the followingdigital filters applied to the signals S_(j): $\begin{matrix}{{F_{1}(S)} = {{\sum\limits_{j = 1}^{4}\quad {ɛ_{j}\frac{S_{j}}{P_{j}^{\prime}\xi_{j}^{\prime 2}}}} = {{\left( {{A_{1}}^{2} + {A_{2}}^{2}} \right){\sum\limits_{j = 1}^{4}\quad {{ɛ_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}}} +}}} & (7) \\{\quad {{\left( {{B_{1}}^{2} + {B_{2}}^{2}} \right){\sum\limits_{j = 1}^{4}\quad {{ɛ_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\zeta_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}}} +}\quad} & \quad \\{\quad {{\left( {{C_{1}}^{2} + {C_{2}}^{2}} \right){\sum\limits_{j = 1}^{4}\quad {{ɛ_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\eta_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}}} +}\quad} & \quad \\{\quad {{2{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}{\sum\limits_{j = 1}^{4}{\left( \frac{P_{j}}{P_{j}^{\prime}} \right)\left( \frac{\xi_{j}\eta_{j}}{\xi_{j}^{\prime 2}} \right)}}} +}\quad} & \quad \\{\quad {{2\left( \frac{A_{2}}{A_{1}} \right)\left( \frac{C_{2}}{C_{1}} \right){A_{1}}{C_{1}}\sin \quad \phi_{A_{1}C_{1}}{\sum\limits_{j = 1}^{4}{ɛ_{j}{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}\eta_{j}}{\xi_{j}^{\prime 2}} \right)}}} +}} & \quad \\{\quad {{2{A_{1}}{B_{1}}{\sum\limits_{j = 1}^{4}\quad {{ɛ_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}\zeta_{j}}{\xi_{j}^{\prime 2}} \right)\cos \quad \phi_{A_{1}B_{1}ɛ_{j}}}}} +}\quad} & \quad \\{\quad {{2{A_{2}}{B_{2}}{\sum\limits_{j = 1}^{4}\quad {{ɛ_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}\zeta_{j}}{\xi_{j}^{\prime 2}} \right)\cos \quad \phi_{A_{2}B_{2}\gamma_{j}}}}} +}\quad} & \quad \\{\quad {{2{B_{1}}{C_{1}}{\sum\limits_{j = 1}^{4}{\left( \frac{P_{j}}{P_{j}^{\prime}} \right)\left( \frac{\zeta_{j}\eta_{j}}{\xi_{j}^{\prime 2}} \right)\cos \quad \phi_{B_{1}C_{1}ɛ_{j}}}}} +}\quad} & \quad \\{\quad {{2{B_{2}}{C_{2}}{\sum\limits_{j = 1}^{4}\quad {ɛ_{j}{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\zeta_{j}\eta_{j}}{\xi_{j}^{\prime 2}} \right)\cos \quad \phi_{B_{2}C_{2}\gamma_{j}}}}},}\quad} & \quad \\{{and}\quad} & \quad \\{{F_{2}(S)} = {{\sum\limits_{j = 1}^{4}\quad {\gamma_{j}\frac{S_{j}}{P_{j}^{\prime}\xi_{j}^{\prime 2}}}} = {{\left( {{A_{1}}^{2} + {A_{2}}^{2}} \right){\sum\limits_{j = 1}^{4}{{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}}} +}}} & (8) \\{\quad {{\left( {{B_{1}}^{2} + {B_{2}}^{2}} \right){\sum\limits_{j = 1}^{4}{{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\zeta_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}}} +}\quad} & \quad \\{\quad {{\left( {{C_{1}}^{2} + {C_{2}}^{2}} \right){\sum\limits_{j = 1}^{4}{{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\eta_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}}} +}\quad} & \quad \\{\quad {{2{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}{\sum\limits_{j = 1}^{4}{ɛ_{j}{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}\eta_{j}}{\xi_{j}^{\prime 2}} \right)}}} +}\quad} & \quad \\{\quad {{2\left( \frac{A_{2}}{A_{1}} \right)\left( \frac{C_{2}}{C_{1}} \right){A_{1}}{C_{1}}\sin \quad \phi_{A_{1}C_{1}}{\sum\limits_{j = 1}^{4}{\left( \frac{P_{j}}{P_{j}^{\prime}} \right)\left( \frac{\xi_{j}\eta_{j}}{\xi_{j}^{\prime 2}} \right)}}} +}} & \quad \\{\quad {{2{A_{1}}{B_{1}}{\sum\limits_{j = 1}^{4}\quad {{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}\zeta_{j}}{\xi_{j}^{\prime 2}} \right)\cos \quad \phi_{A_{1}B_{1}ɛ_{j}}}}} +}\quad} & \quad \\{\quad {{2{A_{2}}{B_{2}}{\sum\limits_{j = 1}^{4}\quad {{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}\zeta_{j}}{\xi_{j}^{\prime 2}} \right)\cos \quad \phi_{A_{2}B_{2}\gamma_{j}}}}} +}\quad} & \quad \\{\quad {{2{B_{1}}{C_{1}}{\sum\limits_{j = 1}^{4}{ɛ_{j}{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\zeta_{j}\eta_{j}}{\xi_{j}^{\prime 2}} \right)\cos \quad \phi_{B_{1}C_{1}ɛ_{j}}}}} +}\quad} & \quad \\{\quad {2{B_{2}}{C_{2}}{\sum\limits_{j = 1}^{4}{\left( \frac{P_{j}}{P_{j}^{\prime}} \right)\left( \frac{\zeta_{j}\eta_{j}}{\xi_{j}^{\prime 2}} \right)\cos \quad \phi_{B_{2}C_{2}\gamma_{j}}}}}\quad} & \quad\end{matrix}$

[0091] wherein ξ′_(j) and P′_(j) are values used in the digital filtersto represent ξ_(j) and P_(j).

[0092] The parameter $\begin{matrix}\left\lbrack {\left( \frac{A_{2}}{A_{1}} \right)\left( \frac{C_{2}}{C_{1}} \right)} \right\rbrack & (9)\end{matrix}$

[0093] in Equations (7) and (8) needs to be determined in order completethe determination of a conjugated quadratures. The parameter given inEquation (9) can be measured for example by introducing π/2 phase shiftsinto the relative phase of the reference beam and the measurement beamand repeating the measurement for the conjugated quadratures. The ratioof the amplitudes of the conjugated quadratures corresponding to (sinφ_(A) ₁ _(C) ₁ /cos φ_(A) ₁ _(C) ₁ ) from the first measurement dividedby the ratio of the amplitudes of the conjugated quadraturescorresponding to (sin φ_(A) ₁ _(C) ₁ /cos φ_(A) ₁ _(C) ₁ ) from thesecond measurement is equal to $\begin{matrix}{\left\lbrack {\left( \frac{A_{2}}{A_{1}} \right)\left( \frac{C_{2}}{C_{1}} \right)} \right\rbrack^{2}.} & (10)\end{matrix}$

[0094] Note that certain of the factors in Equations (7) and (8) havenominal values of 4 within scale factors, e.g., $\begin{matrix}{{{\sum\limits_{j = 1}^{4}{\left( \frac{P_{j}}{P_{j}^{\prime}} \right)\left( \frac{\xi_{j}\eta_{j}}{\xi_{j}^{\prime 2}} \right)}} \simeq 4},{{\sum\limits_{j = 1}^{4}{\left( \frac{P_{j}}{P_{j}^{\prime}} \right)\left( \frac{\zeta_{j}\eta_{j}}{\xi_{j}^{\prime 2}} \right)}} \simeq 4.}} & (11)\end{matrix}$

[0095] The scale factors correspond to the average values for the ratiosof ξ′_(j)/η_(j) and ξ′_(j)/ζ_(j), respectively, assuming that theaverage value of P_(j)/P′_(j)≅1. Certain other of the factors inEquations (7) and (8) have nominal values of zero, e.g., $\begin{matrix}\begin{matrix}{{{\sum\limits_{j = 1}^{4}{{ɛ_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}} \simeq 0},} & {{{\sum\limits_{j = 1}^{4}{{ɛ_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\zeta_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}} \simeq 0},} \\{{{\sum\limits_{j = 1}^{4}{{ɛ_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\eta_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}} \simeq 0},} & \quad \\{{{\sum\limits_{j = 1}^{4}{{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}} \simeq 0},} & {{{\sum\limits_{j = 1}^{4}{{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\zeta_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}} \simeq 0},} \\{{{\sum\limits_{j = 1}^{4}{{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\eta_{j}^{2}}{\xi_{j}^{\prime 2}} \right)}} \simeq 0},} & \quad \\{{\sum\limits_{j = 1}^{4}{ɛ_{j}{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}\eta_{j}}{\xi_{j}^{\prime 2}} \right)}} \simeq 0.} & \quad\end{matrix} & (12)\end{matrix}$

[0096] The remaining factors, $\begin{matrix}\begin{matrix}{{\sum\limits_{j = 1}^{4}{{ɛ_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}\zeta_{j}}{\xi_{j}^{\prime \quad 2}} \right)\cos \quad \phi_{A_{1}B_{1}ɛ_{j}}}},{\sum\limits_{j = 1}^{4}{{ɛ_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}\zeta_{j}}{\xi_{j}^{\prime \quad 2}} \right)\cos \quad \phi_{A_{2}B_{2}\gamma_{j}}}},} \\{{\sum\limits_{j = 1}^{4}{\left( \frac{P_{j}}{P_{j}^{\prime}} \right)\left( \frac{\zeta_{j}\eta_{j}}{\xi_{j}^{\prime \quad 2}} \right)\cos \quad \phi_{B_{1}C_{1}ɛ_{j}}}},{\sum\limits_{j = 1}^{4}{ɛ_{j}{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\zeta_{j}\eta_{j}}{\xi_{j}^{\prime \quad 2}} \right)\cos \quad \phi_{B_{2}C_{2}\gamma_{j}}}},} \\{{\sum\limits_{j = 1}^{4}{{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}\zeta_{j}}{\xi_{j}^{\prime \quad 2}} \right)\cos \quad \phi_{A_{1}B_{1}ɛ_{j}}}},{\sum\limits_{j = 1}^{4}{{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\xi_{j}\zeta_{j}}{\xi_{j}^{\prime \quad 2}} \right)\cos \quad \phi_{A_{2}B_{2}\gamma_{j}}}},} \\{{\sum\limits_{j = 1}^{4}{ɛ_{j}{\gamma_{j}\left( \frac{P_{j}}{P_{j}^{\prime}} \right)}\left( \frac{\zeta_{j}\eta_{j}}{\xi_{j}^{\prime \quad 2}} \right)\cos \quad \phi_{B_{1}C_{1}ɛ_{j}}}},{\sum\limits_{j = 1}^{4}{\left( \frac{P_{j}}{P_{j}^{\prime}} \right)\left( \frac{\zeta_{j}\eta_{j}}{\xi_{j}^{\prime \quad 2}} \right)\cos \quad \phi_{B_{2}C_{2}\gamma_{j}}}},}\end{matrix} & (13)\end{matrix}$

[0097] will have nominal magnitudes ranging from approximately zero toapproximately 4 times a cosine factor and either the average value offactor (P_(j)/P′_(J))(ξ_(j)ζ_(j)/ξ′_(j) ²) or(P_(j)/P′_(J))(ζ_(j)η_(j)/ξ′_(j) ²) depending on the propertiesrespective phases. For the portion of the back ground with phases thatdo not track to a first approximation the phases of the measurementbeams, the magnitudes of all of the terms listed in the Equation (13)will be approximately zero. For the portion of the background withphases that do track to a first approximation the phases of therespective measurement beams, the magnitudes of the terms listed inEquation (13) will be approximately 4 times a cosine factor and eitherthe average value of factor (P_(j)/P′_(J))(ξ_(j)ζ_(j)/ξ′_(j) ²) and orfactor (P_(j)/P′_(J)) (ζ_(j)ηn_(j)/ξ′_(j) ²).

[0098] The two largest terms in Equations (7) and (8) are generally theterms that have the factors (|A₁|²+|A₂|²) and (|B₁|²+|B₂|²). However,the corresponding terms are substantially eliminated by selection ofξ′_(j) values for the terms that have (|A₁|²+|A₂|²) as a factor and bythe design of ζ_(j) values for the terms that have (|B₁|²+|B₂|²) as afactor as shown in Equation (12).

[0099] The largest contribution from effects of background isrepresented by the contribution to the interference term between thereference beam and the portion of the background beam generated by themeasurement beam component of beam 28. This portion of the effect of thebackground can be measured by measuring the corresponding conjugatedquadratures of the portion of the background with the return measurementbeam component of beam 32 set equal to zero, i.e., measuring therespective electrical interference signals S_(j) with substrate 60removed and with either |A₂|=0 or |A₁|=0 and visa versa. The measuredconjugated quadratures of the portion of the effect of the backgroundcan than used to compensate for the respective background effectsbeneficially in an end use application if required.

[0100] Information about the largest contribution from effects ofbackground amplitude 2ξ_(j)ζ_(j)|A₁| |B₁| and phase φ_(A) ₁ _(B) ₁ _(ε)_(j) , i.e., the interference term between the reference beam and theportion of background beam generated by the measurement beam componentof beam 28, may be obtained by measuring S_(j) for j=1,2,3,4 as afunction of relative phase shift between reference beam and themeasurement beam component of beam 28 with substrate 60 removed andeither |A₂|=0 or |A₁|=0 and visa versa and Fourier analyzing themeasured values of S_(j). Such information can be used to help identifythe origin of the respective background.

[0101] Other techniques may be incorporated into other embodiments toreduce and/or compensate for the effects of background beams withoutdeparting from either the scope or spirit of the present invention suchas described in commonly owned U.S. Pat. Nos. 5,760,901 entitled “MethodAnd Apparatus For Confocal Interference Microscopy With BackgroundAmplitude Reduction and Compensation,” 5,915,048 entitled “Method andApparatus for Discrimination In-Focus Images from Out-of-Focus LightSignals from Background and Foreground Light Sources,” and 6,480,285 B1wherein each of the three patents are by Henry A. Hill. The contents ofeach of the three cited patents are herein incorporated in theirentirety by reference.

[0102] The selection of values for ξ′_(j) based on information aboutcoefficients ξ_(j) for j=1,2,3,4 that may be obtained by measuring theS_(j) for j=1,2,3,4 with only the reference beam present in theinterferometer system. In certain embodiments, this may correspondsimply blocking the measurement beam components of input beam 24 and incertain other embodiments, this may correspond to simply measuring theS_(j) for j=1,2,3,4 with substrate 60 removed. A test of the correctnessof a set of values for ξ′_(j) is the degree to which the (|A₁|²+|A₂|²)terms in Equations (7) and (8) are zero.

[0103] Information about coefficients ξ_(j)η_(j) for j=1,2,3,4 may beobtained by scanning an artifact past the spots corresponding to therespective four conjugate detector pixels with either |A₂|=0 or |A₁|=0and measuring the conjugated quadratures component 2|A₁| |C₁| cos φ_(A)₁ _(C) ₁ or 2|A₁| |C₁| sin φ_(A) ₁ _(C) ₁ , respectively. A change inthe amplitude of the 2|A₁| |C₁| cos φ_(A) ₁ _(C) _(1 l) or 2|A₁| |C₁|sin φ_(A) ₁ _(C) ₁ term corresponds to a variation in ξ_(j)η_(j) as afunction of j. Information about the coefficients ξ_(j)η_(j) forj=1,2,3,4 may be used for example to monitor the stability of one ormore elements of interferometer system 10.

[0104] The bi-homodyne detection method is a robust technique for thedetermination of conjugated quadratures of fields. First, the conjugatedquadratures |C₁| cos φ_(A) ₁ _(C) ₁ and |C₁| sin φ_(A) ₁ _(C) ₁ are theprimary terms in the digitally filtered values F₁ (S) and F₂ (S),respectively, since as noted in the discussion with respect to Equation(12), the terms with the factors (|A₁|²+|A₂|²) and (|B₁|²+|B₂|²) aresubstantially zero.

[0105] Secondly, the coefficients of |C₁| cos φ_(A) ₁ _(C) ₁ and |C₂|sin φ_(A) ₁ _(C) ₁ terms in Equations (7) and (8) are identical. Thushighly accurate measurements of the interference terms between thereturn measurement beam and the reference beam with respect toamplitudes and phases, i.e., highly accurate measurements of conjugatedquadratures of fields can be measured wherein first order variations inξ_(j) and first order errors in normalizations such as (P_(j)/P′_(j))and (ξ_(j) ²/ξ′_(j) ²) enter in only second or higher order. Thisproperty translates into a significant advantage. Also, thecontributions to each component of the conjugated quadratures |C₁| cosφ_(A) ₁ _(C) ₁ and |C₁| sin φ_(A) ₁ _(C) ₁ from a respective set of fourelectrical interference signal values have the same window function andthus are obtained as jointly determined values.

[0106] Other distinguishing features of the bi-homodyne technique areevident in Equations (7) and (8): the coefficients of the conjugatedquadratures |C₁| cos φ_(A) ₁ _(C) ₁ and |C₁| sin φ_(A) ₁ _(C) ₁ inEquations (7) and (8), respectively, corresponding to the first equationof Equations (11) are identical independent of errors in assumed valuesfor ξ_(j) and η_(j); the coefficients of the conjugated quadratures |C₁|sin φ_(A) ₁ _(C) ₁ and |C₁| cos φ_(A) ₁ _(C) ₁ in Equations (7) and(8),respectively, corresponding to the fourth equation of Equations (12) areidentical independent of errors in assumed values for ξ′_(j). Thushighly accurate values of the phases corresponding to conjugatedquadratures can be measured with first order variations in ξ_(j) andfirst order errors in normalizations such as (P_(j)/P′_(j)) and (ξ_(j)²/ξ′_(j) ²) enter in only through some high order effect.

[0107] It is also evident that since the conjugated quadratures offields are obtained jointly when using the bi-homodyne detection method,there is a significant reduction in the potential for an error intracking phase as a result of a phase redundancy unlike the situationpossible in single-homodyne detection of conjugated quadratures offields.

[0108] There are a number of advantages of the bi-homodyne detection asa consequence of the conjugated quadratures of fields being jointlyacquired quantities. One advantage is a reduced sensitivity the effectsof an overlay error of a spot in or on the substrate that is beingimaged and a conjugate image of conjugate pixel of a multi-pixeldetector during the acquisition of four electrical interference signalvalues of each spot in and/or on a substrate imaged usinginterferometric confocal microscopy. Overlay errors are errors in theset of four conjugate images of a respective set of conjugate detectorpixels relative to the spot being imaged.

[0109] Another advantage is that when operating in the scanning modethere is a reduced sensitivity to effects of pinhole-to-pinholevariations in properties of a conjugate set of pinholes used in aconfocal microscopy system that are conjugate to a spot in or on thesubstrate being imaged at different times during the scan.

[0110] Another advantage is that when operating in the scanning modethere is a reduced sensitivity to effects of pixel-to-pixel variation ofproperties within a set of conjugate pixels that are conjugate to a spotin or on the substrate being imaged at different times during the scan.

[0111] Another advantage is that when operating in the scanning modethere is reduced sensitivity to effects of pulse-to-pulse variations ofa respective conjugate set of pulses of the input beam 24 to theinterferometer system.

[0112] The pinholes and pixels of a multi-pixel detector of a set ofconjugate pinholes and conjugate pixels of a multi-pixel detector maycomprise contiguous pinholes of an array of pinholes and/or contiguouspixels of a multi-pixel detector or may comprise selected pinholes froman array of pinholes and/or pixels from an array of pixels wherein theseparation between the selected pinholes is an integer number of pinholeseparations and the separation between an array of respective pixelscorresponds to an integer number of pixel separations without loss oflateral and/or longitudinal resolution and signal-to-noise ratios. Thecorresponding scan rate would be equal to the integer times the spacingof spots on the measurement object 60 conjugate to set of conjugatepinholes and/or set of conjugate pixels divided by the read out rate ofthe multi-pixel detector. This property permits a significant increasein through put for an interferometric confocal microscope with respectto the number of spots in and/or on a substrate imaged per unit time.

[0113] Referring to the quad-homodyne detection method, a set of fourelectrical interference signal values is obtained for each spot onand/or in substrate 60 being imaged with two pulse sequences from source18 and beam-conditioner beam-conditioner 22. The set of four electricalinterference signal values S_(j), j=1,2,3,4 used for obtainingconjugated quadratures of fields for a single a spot on and/or in asubstrate being imaged is represented for the quad-homodyne detectionwithin a scale factor by the formulae $\begin{matrix}{{S_{1} = {P_{1}\begin{Bmatrix}\begin{matrix}\begin{matrix}{{\xi_{1}^{2}{A_{1}}^{2}} + {\zeta_{1}^{2}{B_{1}}^{2}} + {\eta_{1}^{2}{C_{1}}^{2}} + {\zeta_{1}\eta_{1}2{B_{1}}{C_{1}}\cos \quad \phi_{B_{1}C_{1}ɛ_{1}}} +} \\{{\xi_{1}\zeta_{1}2{A_{1}}{B_{1}}\cos \quad \phi_{A_{1}B_{1}ɛ_{1}}} + {ɛ_{1}\xi_{1}\eta_{1}2{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}} +}\end{matrix} \\{{\xi_{1}^{2}{A_{2}}^{2}} + {\zeta_{1}^{2}{B_{2}}^{2}} + {\eta_{1}^{2}{C_{2}}^{2}} + {\zeta_{1}\eta_{1}2{B_{2}}{C_{2}}\cos \quad \phi_{B_{2}C_{2}\gamma_{1}}} +}\end{matrix} \\{{\xi_{1}\zeta_{1}2{A_{2}}{B_{2}}\cos \quad \phi_{A_{2}B_{2}\gamma_{1}}} + {\gamma_{1}\xi_{1}\eta_{1}2{A_{2}}{C_{2}}\cos \quad \phi_{A_{2}C_{2}}}}\end{Bmatrix}}},} & (14) \\{{S_{2} = {P_{1}\begin{Bmatrix}\begin{matrix}\begin{matrix}{{\xi_{2}^{2}{A_{3}}^{2}} + {\zeta_{2}^{2}{B_{3}}^{2}} + {\eta_{2}^{2}{C_{3}}^{2}} + {\zeta_{2}\eta_{2}2{B_{3}}{C_{3}}\cos \quad \phi_{B_{3}C_{3}ɛ_{2}}} +} \\{{\xi_{2}\zeta_{2}2{A_{3}}{B_{3}}\cos \quad \phi_{A_{3}B_{3}ɛ_{2}}} + {ɛ_{2}\xi_{2}\eta_{2}2{A_{3}}{C_{3}}\cos \quad \phi_{A_{3}C_{3}}} +}\end{matrix} \\{{\xi_{2}^{2}{A_{4}}^{2}} + {\zeta_{2}^{2}{B_{4}}^{2}} + {\eta_{2}^{2}{C_{4}}^{2}} + {\zeta_{2}\eta_{2}2{B_{4}}{C_{4}}\cos \quad \phi_{B_{4}C_{4}\gamma_{2}}} +}\end{matrix} \\{{\xi_{2}\zeta_{2}2{A_{4}}{B_{4}}\cos \quad \phi_{A_{4}B_{4}\gamma_{2}}} + {\gamma_{2}\xi_{2}\eta_{2}2{A_{4}}{C_{4}}\cos \quad \phi_{A_{4}C_{4}}}}\end{Bmatrix}}},} & (15) \\{{S_{3} = {P_{2}\begin{Bmatrix}\begin{matrix}\begin{matrix}{{\xi_{1}^{2}{A_{1}}^{2}} + {\zeta_{1}^{2}{B_{1}}^{2}} + {\eta_{1}^{2}{C_{1}}^{2}} + {\zeta_{1}\eta_{1}2{B_{1}}{C_{1}}\cos \quad \phi_{B_{1}C_{1}ɛ_{3}}} +} \\{{\xi_{1}\zeta_{1}2{A_{1}}{B_{1}}\cos \quad \phi_{A_{1}B_{1}ɛ_{3}}} + {ɛ_{3}\xi_{1}\eta_{1}2{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}} +}\end{matrix} \\{{\xi_{1}^{2}{A_{2}}^{2}} + {\zeta_{1}^{2}{B_{2}}^{2}} + {\eta_{1}^{2}{C_{2}}^{2}} + {\zeta_{1}\eta_{1}2{B_{2}}{C_{2}}\cos \quad \phi_{B_{2}C_{2}\gamma_{3}}} +}\end{matrix} \\{{\xi_{1}\zeta_{1}2{A_{2}}{B_{2}}\cos \quad \phi_{A_{2}B_{2}\gamma_{3}}} + {\gamma_{3}\xi_{1}\eta_{1}2{A_{2}}{C_{2}}\cos \quad \phi_{A_{2}C_{2}}}}\end{Bmatrix}}},} & (16) \\{{S_{4} = {P_{2}\begin{Bmatrix}\begin{matrix}\begin{matrix}{{\xi_{2}^{2}{A_{3}}^{2}} + {\zeta_{2}^{2}{B_{3}}^{2}} + {\eta_{2}^{2}{C_{3}}^{2}} + {\zeta_{2}\eta_{2}2{B_{3}}{C_{3}}\cos \quad \phi_{B_{3}C_{3}ɛ_{4}}} +} \\{{\xi_{2}\zeta_{2}2{A_{3}}{B_{3}}\cos \quad \phi_{A_{3}B_{3}ɛ_{4}}} + {ɛ_{4}\xi_{2}\eta_{2}2{A_{3}}{C_{3}}\cos \quad \phi_{A_{3}C_{3}}} +}\end{matrix} \\{{\xi_{2}^{2}{A_{4}}^{2}} + {\zeta_{2}^{2}{B_{4}}^{2}} + {\eta_{2}^{2}{C_{4}}^{2}} + {\zeta_{2}\eta_{2}2{B_{4}}{C_{4}}\cos \quad \phi_{B_{4}C_{4}\gamma_{4}}} +}\end{matrix} \\{{\xi_{2}\zeta_{2}2{A_{4}}{B_{4}}\cos \quad \phi_{A_{4}B_{4}\gamma_{4}}} + {\gamma_{4}\xi_{2}\eta_{2}2{A_{4}}{C_{4}}\cos \quad \phi_{A_{4}C_{4}}}}\end{Bmatrix}}},} & (17)\end{matrix}$

[0114] where coefficients A₁, A₂, A₃, and A₄ represent the amplitudes ofthe reference beams corresponding to the first, second, third, andfourth frequency components, respectively, of input beam 24;coefficients B₁, B₂, B₃, and B₄ represent the 10 amplitudes ofbackground beams corresponding to reference beams A₁, A₂, A₃, and A₄,respectively; coefficients C₁, C₂, C₃, and C₄ represent the amplitudesof the return measurement beams corresponding to reference beams A₁, A₂,A₃, and A₄, respectively; P₁ and P₂ represent the integrated intensitiesof the first frequency component in the first and second pulsesequences, respectively, of the input beam 24; and the values for ε_(j)and γ_(j) are listed in Table 1. The description of the coefficientsξ_(j), ζ_(j), and η_(j) for the quad-homodyne detection method is thesame as the corresponding portion of the description given for ε_(j),ζ_(j), and η_(j) of the bi-homodyne detection method.

[0115] It is assumed in Equations (14), (15), (16), and (17) that theratios of |A₂|/|A₁ and |A₄|/|A₃| are not dependent on j or the value ofP_(j). In order to simplify the representation of S_(j) so as to projectthe important features without departing from either the scope or spiritof the present invention, it is also assumed in Equations (14), (15),(16), and (17) that the ratios of the amplitudes of the returnmeasurement beams corresponding to |A₂|/|A₁| and |A₄|/|A₃| are notdependent on j or the value of P_(j). However, the ratios |C₂|/|C₁| and|C₄|/|C₃| will be different from the ratios |A₂|/|A₁| and |A₄|/|A₃|,respectively, when the ratio of the amplitudes of the measurement beamcomponents corresponding to |A₂|/|A₁ and |A₄|/|A₃|, respectively, aredifferent from the ratios |A₂ |/|A₁| and |A₄|/|A₃, respectively.

[0116] Noting that cos φ_(A) ₂ _(C) ₂ =±sin φ_(A) ₁ _(C) ₁ by thecontrol of the relative phase shifts between corresponding reference andmeasurement beam components in beam 32, Equations (14), (15), (16), and(17) may be written, respectively, as $\begin{matrix}{{S_{1} = {P_{1}\begin{Bmatrix}\begin{matrix}\begin{matrix}{{\xi_{1}^{2}\left( {{A_{1}}^{2} + {A_{2}}^{2}} \right)} + {\zeta_{1}^{2}\left( {{B_{1}}^{2} + {B_{2}}^{2}} \right)} + {\eta_{1}^{2}\left( {{C_{1}}^{2} + {C_{2}}^{2}} \right)} +} \\{{2\zeta_{1}{\eta_{1}\left\lbrack {{{B_{1}}{C_{1}}\cos \quad \phi_{B_{1}C_{1}ɛ_{1}}} + {{B_{2}}{C_{2}}\cos \quad \phi_{B_{2}C_{2}\gamma_{1}}}} \right\rbrack}} +}\end{matrix} \\{{2\xi_{1}{\eta_{1}\begin{bmatrix}{{ɛ_{1}{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}} +} \\{{\gamma_{1}\left( \frac{A_{2}}{A_{1}} \right)}\left( \frac{C_{2}}{C_{1}} \right){A_{1}}{C_{1}}\sin \quad \phi_{A_{1}C_{1}}}\end{bmatrix}}} +}\end{matrix} \\{2\xi_{1}{\zeta_{1}\left\lbrack {{{A_{1}}{B_{1}}\cos \quad \phi_{A_{1}B_{1}ɛ_{1}}} + {{A_{2}}{B_{2}}\cos \quad \phi_{A_{2}B_{2}\gamma_{1}}}} \right\rbrack}}\end{Bmatrix}}},} & (18) \\{{S_{2} = {P_{1}\begin{Bmatrix}\begin{matrix}\begin{matrix}{{\xi_{2}^{2}\left( {{A_{3}}^{2} + {A_{4}}^{2}} \right)} + {\zeta_{2}^{2}\left( {{B_{3}}^{2} + {B_{4}}^{2}} \right)} + {\eta_{2}^{2}\left( {{C_{3}}^{2} + {C_{4}}^{2}} \right)} +} \\{{2\zeta_{2}{\eta_{2}\left\lbrack {{{B_{3}}{C_{3}}\cos \quad \phi_{B_{3}C_{3}ɛ_{2}}} + {{B_{4}}{C_{4}}\cos \quad \phi_{B_{4}C_{4}\gamma_{2}}}} \right\rbrack}} +}\end{matrix} \\{{2\xi_{2}{\eta_{2}\left( \frac{A_{3}}{A_{1}} \right)}{\left( \frac{C_{3}}{C_{1}} \right)\begin{bmatrix}{{ɛ_{2}{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}} +} \\{{\gamma_{2}\left( \frac{A_{4}}{A_{3}} \right)}\left( \frac{C_{4}}{C_{3}} \right){A_{1}}{C_{1}}\sin \quad \phi_{A_{1}C_{1}}}\end{bmatrix}}} +}\end{matrix} \\{2\xi_{2}{\zeta_{2}\left\lbrack {{{A_{3}}{B_{3}}\cos \quad \phi_{A_{3}B_{3}ɛ_{2}}} + {{A_{4}}{B_{4}}\cos \quad \phi_{A_{4}B_{4}\gamma_{2}}}} \right\rbrack}}\end{Bmatrix}}},} & (19) \\{{S_{3} = {P_{2}\begin{Bmatrix}\begin{matrix}\begin{matrix}{{\xi_{1}^{2}\left( {{A_{1}}^{2} + {A_{2}}^{2}} \right)} + {\zeta_{1}^{2}\left( {{B_{1}}^{2} + {B_{2}}^{2}} \right)} + {\eta_{1}^{2}\left( {{C_{1}}^{2} + {C_{2}}^{2}} \right)} +} \\{{2\zeta_{1}{\eta_{1}\left\lbrack {{{B_{1}}{C_{1}}\cos \quad \phi_{B_{1}C_{1}ɛ_{3}}} + {{B_{2}}{C_{2}}\cos \quad \phi_{B_{2}C_{2}\gamma_{3}}}} \right\rbrack}} +}\end{matrix} \\{{2\xi_{1}{\eta_{1}\begin{bmatrix}{{ɛ_{3}{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}} +} \\{{\gamma_{3}\left( \frac{A_{2}}{A_{1}} \right)}\left( \frac{C_{2}}{C_{1}} \right){A_{1}}{C_{1}}\sin \quad \phi_{A_{1}C_{1}}}\end{bmatrix}}} +}\end{matrix} \\{2\xi_{1}{\zeta_{1}\left\lbrack {{{A_{1}}{B_{1}}\cos \quad \phi_{A_{1}B_{1}ɛ_{3}}} + {{A_{2}}{B_{2}}\cos \quad \phi_{A_{2}B_{2}\gamma_{3}}}} \right\rbrack}}\end{Bmatrix}}},} & (20) \\{{S_{4} = {P_{2}\begin{Bmatrix}\begin{matrix}\begin{matrix}{{\xi_{2}^{2}\left( {{A_{3}}^{2} + {A_{4}}^{2}} \right)} + {\zeta_{2}^{2}\left( {{B_{3}}^{2} + {B_{4}}^{2}} \right)} + {\eta_{2}^{2}\left( {{C_{3}}^{2} + {C_{4}}^{2}} \right)} +} \\{{2\zeta_{2}{\eta_{2}\left\lbrack {{{B_{3}}{C_{3}}\cos \quad \phi_{B_{3}C_{3}ɛ_{4}}} + {{B_{4}}{C_{4}}\cos \quad \phi_{B_{4}C_{4}\gamma_{4}}}} \right\rbrack}} +}\end{matrix} \\{{2\xi_{2}{\eta_{2}\left( \frac{A_{3}}{A_{1}} \right)}{\left( \frac{C_{3}}{C_{1}} \right)\begin{bmatrix}{{ɛ_{4}{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}} +} \\{{\gamma_{4}\left( \frac{A_{4}}{A_{3}} \right)}\left( \frac{C_{4}}{C_{3}} \right){A_{1}}{C_{1}}\sin \quad \phi_{A_{1}C_{1}}}\end{bmatrix}}} +}\end{matrix} \\{2\xi_{2}{\zeta_{2}\left\lbrack {{{A_{3}}{B_{3}}\cos \quad \phi_{A_{3}B_{3}ɛ_{4}}} + {{A_{4}}{B_{4}}\cos \quad \phi_{A_{4}B_{4}\gamma_{4}}}} \right\rbrack}}\end{Bmatrix}}},} & (21)\end{matrix}$

[0117] where the relationship cos φ_(A) ₂ _(C) ₂ =sin φ_(A) ₁ _(C) ₁ hasbeen used without departing from either the scope or spirit of thepresent invention.

[0118] Information about the conjugated quadratures |C₁| cos φ_(A) ₁_(C) ₁ and |C₁| sin φ_(A) ₁ _(C) ₁ are obtained using the symmetric andantisymmetric properties and orthogonality property of the conjugatedquadratures as represented by the following digital filters applied tothe signal values S_(j): j=1,2,3,4 $\begin{matrix}{{{F_{3}(S)} = {{\left( \frac{1}{P_{1}^{\prime}} \right)\left( {\frac{S_{1}}{\xi_{1}^{\prime 2}} - \frac{S_{2}}{\xi_{2}^{\prime 2}}} \right)} - {\left( \frac{1}{P_{2}^{\prime}} \right)\left( {\frac{S_{3}}{\xi_{1}^{\prime 2}} - \frac{S_{4}}{\xi_{2}^{\prime 2}}} \right)}}},} & (22) \\{{F_{4}(S)} = {{\left( \frac{1}{P_{1}^{\prime}} \right)\left( {\frac{S_{1}}{\xi_{1}^{\prime 2}} - \frac{S_{2}}{\xi_{2}^{\prime 2}}} \right)} + {\left( \frac{1}{P_{2}^{\prime}} \right){\left( {\frac{S_{3}}{\xi_{1}^{\prime 2}} - \frac{S_{4}}{\xi_{2}^{\prime 2}}} \right).}}}} & (23)\end{matrix}$

[0119] The description of ξ′_(j) and P′_(j) for the quad-homodynedetection method is the same as the corresponding description given forξ′_(j) and P′_(j) in the bi-homodyne detection method. Using Equations(18), (19), (20), (21), (22), and (23), the following expressions areobtained for the filtered quantities containing components of theconjugated quadratures $\begin{matrix}{{C_{1}}\cos \quad \phi_{A_{1}C_{1}}\quad {and}} & \quad \\{{C_{1}}\quad \sin \quad \phi_{A_{1}C_{1}}\text{:}} & \quad \\{{F_{3}(S)} = {{\left( {\frac{P_{1}}{P_{1}^{\prime}} - \frac{P_{2}}{P_{2}^{\prime}}} \right)\left\lbrack {{\left( {{A_{1}}^{2} + {A_{2}}^{2}} \right)\left( \frac{\xi_{1}^{2}}{\xi_{1}^{\prime 2}} \right)} - {\left( {{A_{3}}^{2} + {A_{4}}^{2}} \right)\left( \frac{\xi_{2}^{2}}{\xi_{2}^{\prime 2}} \right)}} \right\rbrack} +}} & (24) \\{{~~~~~~~~~~~~~~~~~}{{\left( {\frac{P_{1}}{P_{1}^{\prime}} - \frac{P_{2}}{P_{2}^{\prime}}} \right)\left\lbrack {{\left( {{B_{1}}^{2} + {B_{2}}^{2}} \right)\left( \frac{\zeta_{1}^{2}}{\xi_{1}^{\prime 2}} \right)} - {\left( {{B_{3}}^{2} + {B_{4}}^{2}} \right)\left( \frac{\zeta_{2}^{2}}{\xi_{2}^{\prime 2}} \right)}} \right\rbrack} +}} & \quad \\{{~~~~~~~~~~~~~~~~~}{{\left( {\frac{P_{1}}{P_{1}^{\prime}} - \frac{P_{2}}{P_{2}^{\prime}}} \right)\left\lbrack {{\left( {{C_{1}}^{2} + {C_{2}}^{2}} \right)\left( \frac{\eta_{1}^{2}}{\xi_{1}^{\prime 2}} \right)} - {\left( {{C_{3}}^{2} + {C_{4}}^{2}} \right)\left( \frac{\eta_{2}^{2}}{\xi_{2}^{\prime 2}} \right)}} \right\rbrack} +}} & \quad \\{{~~~~~~~~~~~~~~~~~}{2{\left( {\frac{P_{1}}{P_{1}^{\prime}} + \frac{P_{2}}{P_{2}^{\prime}}} \right)\left\lbrack {\left( \frac{\xi_{1}\eta_{1}}{\xi_{1}^{\prime 2}} \right) + {\left( \frac{\xi_{2}\eta_{2}}{\xi_{2}^{\prime 2}} \right)\left( \frac{A_{3}}{A_{1}} \right)\left( \frac{C_{3}}{C_{1}} \right)}} \right\rbrack}}} & \quad \\{{~~~~~~~~~~~~~~~~~}{{{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}} +}} & \quad \\{{~~~~~~~~~~~~~~~~}{2\left( {\frac{P_{1}}{P_{1}^{\prime}} - \frac{P_{2}}{P_{2}^{\prime}}} \right)\left( \frac{A_{2}}{A_{1}} \right){\left( \frac{C_{2}}{C_{1}} \right)\begin{bmatrix}{\left( \frac{\xi_{1}\eta_{1}}{\xi_{1}^{\prime 2}} \right) +} \\{\left( \frac{\xi_{2}\eta_{2}}{\xi_{2}^{\prime 2}} \right)\left( \frac{A_{4}}{A_{2}} \right)\left( \frac{C_{4}}{C_{2}} \right)}\end{bmatrix}}}} & \quad \\{\quad {{{A_{1}}{C_{1}}\sin \quad \phi_{A_{1}C_{1}}} +}} & \quad \\{{~~~~~~~~~~~~~~~~~}{{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{A_{1}B_{1}ɛ_{1}}} - {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{A_{1}B_{1}ɛ_{3}}}} \right)\frac{\xi_{1}\zeta_{1}}{\xi_{1}^{\prime 2}}{A_{1}}{B_{1}}} -}} & \quad \\{{~~~~~~~~~~~~~~~~~}{{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{A_{3}B_{3}ɛ_{2}}} - {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{A_{3}B_{3}ɛ_{4}}}} \right)\frac{\xi_{2}\zeta_{2}}{\xi_{2}^{\prime 2}}{A_{3}}{B_{3}}} +}} & \quad \\{\quad {{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{A_{2}B_{2}\gamma_{1}}} - {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{A_{2}B_{2}\gamma_{3}}}} \right)\frac{\xi_{1}\zeta_{1}}{\xi_{1}^{\prime 2}}{A_{2}}{B_{2}}} -}} & \quad \\{\quad {{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{A_{4}B_{4}\gamma_{2}}} - {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{A_{4}B_{4}\gamma_{4}}}} \right)\frac{\xi_{2}\zeta_{2}}{\xi_{2}^{\prime 2}}{A_{4}}{B_{4}}} +}} & \quad \\{\quad {{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{B_{1}C_{1}ɛ_{1}}} - {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{B_{1}C_{1}ɛ_{3}}}} \right)\frac{\xi_{1}\zeta_{1}}{\xi_{1}^{\prime 2}}{B_{1}}{C_{1}}} -}} & \quad \\{\quad {{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{B_{3}C_{3}ɛ_{2}}} - {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{B_{3}C_{3}ɛ_{4}}}} \right)\frac{\xi_{2}\zeta_{2}}{\xi_{2}^{\prime 2}}{B_{3}}{C_{3}}} +}} & \quad \\{\quad {{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{B_{2}C_{2}\gamma_{1}}} - {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{B_{2}C_{2}\gamma_{3}}}} \right)\frac{\xi_{1}\zeta_{1}}{\xi_{1}^{\prime 2}}{B_{2}}{C_{2}}} -}} & \quad \\{{~~~~~~~~~~~~~~~~~}{{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{B_{4}C_{4}\gamma_{2}}} - {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{B_{4}C_{4}\gamma_{4}}}} \right)\frac{\xi_{2}\zeta_{2}}{\xi_{2}^{\prime 2}}{B_{4}}{C_{4}}},}} & \quad \\{{F_{4}(S)} = {{\left( {\frac{P_{1}}{P_{1}^{\prime}} + \frac{P_{2}}{P_{2}^{\prime}}} \right)\left\lbrack {{\left( {{A_{1}}^{2} + {A_{2}}^{2}} \right)\left( \frac{\xi_{1}^{2}}{\xi_{1}^{\prime 2}} \right)} - {\left( {{A_{3}}^{2} + {A_{4}}^{2}} \right)\left( \frac{\xi_{2}^{2}}{\xi_{2}^{\prime 2}} \right)}} \right\rbrack} +}} & (25) \\{{~~~~~~~~~~~~~~~~~~~}{{\left( {\frac{P_{1}}{P_{1}^{\prime}} + \frac{P_{2}}{P_{2}^{\prime}}} \right)\left\lbrack {{\left( {{B_{1}}^{2} + {B_{2}}^{2}} \right)\left( \frac{\zeta_{1}^{2}}{\xi_{1}^{\prime 2}} \right)} - {\left( {{B_{3}}^{2} + {B_{4}}^{2}} \right)\left( \frac{\zeta_{2}^{2}}{\xi_{2}^{\prime 2}} \right)}} \right\rbrack} +}} & \quad \\{{~~~~~~~~~~~~~~~~~~~}{{\left( {\frac{P_{1}}{P_{1}^{\prime}} + \frac{P_{2}}{P_{2}^{\prime}}} \right)\left\lbrack {{\left( {{C_{1}}^{2} + {C_{2}}^{2}} \right)\left( \frac{\eta_{1}^{2}}{\xi_{1}^{\prime 2}} \right)} - {\left( {{C_{3}}^{2} + {C_{4}}^{2}} \right)\left( \frac{\eta_{2}^{2}}{\xi_{2}^{\prime 2}} \right)}} \right\rbrack} +}} & \quad \\{\quad {2{\left( {\frac{P_{1}}{P_{1}^{\prime}} - \frac{P_{2}}{P_{2}^{\prime}}} \right)\left\lbrack {\left( \frac{\xi_{1}\eta_{1}}{\xi_{1}^{\prime 2}} \right) + {\left( \frac{\xi_{2}\eta_{2}}{\xi_{2}^{\prime 2}} \right)\left( \frac{A_{3}}{A_{1}} \right)\left( \frac{C_{3}}{C_{1}} \right)}} \right\rbrack}}} & \quad \\{{~~~~~~~~~~~~~~~~~~~~}{{{A_{1}}{C_{1}}\cos \quad \phi_{A_{1}C_{1}}} +}} & \quad \\{{~~~~~~~~~~~~~~~~~~~}{2\left( {\frac{P_{1}}{P_{1}^{\prime}} + \frac{P_{2}}{P_{2}^{\prime}}} \right)\left( \frac{A_{2}}{A_{1}} \right){\left( \frac{C_{2}}{C_{1}} \right)\begin{bmatrix}{\left( \frac{\xi_{1}\eta_{1}}{\xi_{1}^{\prime 2}} \right) +} \\{\left( \frac{\xi_{2}\eta_{2}}{\xi_{2}^{\prime 2}} \right)\left( \frac{A_{4}}{A_{2}} \right)\left( \frac{C_{4}}{C_{2}} \right)}\end{bmatrix}}}} & \quad \\{{~~~~~~~~~~~~~~~~~~~}{{{A_{1}}{C_{1}}\sin \quad \phi_{A_{1}C_{1}}} +}} & \quad \\{{~~~~~~~~~~~~~~~~~~~}{{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{A_{1}B_{1}ɛ_{1}}} + {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{A_{1}B_{1}ɛ_{3}}}} \right)\frac{\xi_{1}\zeta_{1}}{\xi_{1}^{\prime 2}}{A_{1}}{B_{1}}} -}} & \quad \\{\quad {{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{A_{3}B_{3}ɛ_{2}}} + {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{A_{3}B_{3}ɛ_{4}}}} \right)\frac{\xi_{2}\zeta_{2}}{\xi_{2}^{\prime 2}}{A_{3}}{B_{3}}} +}} & \quad \\{{~~~~~~~~~~~~~~~~~~~}{{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{A_{2}B_{2}\gamma_{1}}} + {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{A_{2}B_{2}\gamma_{3}}}} \right)\frac{\xi_{1}\zeta_{1}}{\xi_{1}^{\prime 2}}{A_{2}}{B_{2}}} -}} & \quad \\{{~~~~~~~~~~~~~~~~~~~}{{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{A_{4}B_{4}\gamma_{2}}} + {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{A_{4}B_{4}\gamma_{4}}}} \right)\frac{\xi_{2}\zeta_{2}}{\xi_{2}^{\prime 2}}{A_{4}}{B_{4}}} +}} & \quad \\{{~~~~~~~~~~~~~~~~~~~}{{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{B_{1}C_{1}ɛ_{1}}} + {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{B_{1}C_{1}ɛ_{3}}}} \right)\frac{\xi_{1}\zeta_{1}}{\xi_{1}^{\prime 2}}{B_{1}}{C_{1}}} -}} & \quad \\{\quad {{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{B_{3}C_{3}ɛ_{2}}} + {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{B_{3}C_{3}ɛ_{4}}}} \right)\frac{\xi_{2}\zeta_{2}}{\xi_{2}^{\prime 2}}{B_{3}}{C_{3}}} +}} & \quad \\{\quad {{2\quad \left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{B_{2}C_{2}\gamma_{1}}} + {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{B_{2}C_{2}\gamma_{3}}}} \right)\frac{\xi_{1}\zeta_{1}}{\xi_{1}^{\prime 2}}{B_{2}}{C_{2}}} -}} & \quad \\{{~~~~~~~~~~~~~~~~~~~}{2\left( {{\frac{P_{1}}{P_{1}^{\prime}}\cos \quad \phi_{B_{4}C_{4}\gamma_{2}}} + {\frac{P_{2}}{P_{2}^{\prime}}\cos \quad \phi_{B_{4}C_{4}\gamma_{4}}}} \right)\frac{\xi_{2}\zeta_{2}}{\xi_{2}^{\prime 2}}{B_{4}}{{C_{4}}.}}} & \quad\end{matrix}$

[0120] The parameters $\begin{matrix}{\left\lbrack {\left( \frac{A_{2}}{A_{1}} \right)\left( \frac{C_{2}}{C_{1}} \right)} \right\rbrack,} & (26) \\{{\left( \frac{A_{4}}{A_{2}} \right)\left( \frac{C_{4}}{C_{2}} \right)},} & (27) \\\left\lbrack {\left( \frac{A_{3}}{A_{1}} \right)\left( \frac{C_{3}}{C_{1}} \right)} \right\rbrack & (28)\end{matrix}$

[0121] need to be determined in order to complete the determination of aconjugated quadratures for certain end use applications. The parametersgiven by Equations (26), (27), and (28) can for example be measured byprocedures analogous to the procedure described for the bi-homodynedetection method with respect to measuring the quantity specified byEquation (9).

[0122] The remaining description of the quad-homodyne detection methodis the same as corresponding portion of the description given for thebi-homodyne detection method.

[0123] It is also evident that since the conjugated quadratures offields are obtained jointly when using the quad-homodyne detection,there is a significant reduction in the potential for an error intracking phase as a result of a phase redundancy unlike the situationpossible in single-homodyne detection of conjugated quadratures offields.

[0124] There are a number of advantages of the quad-homodyne detectionas a consequence of the conjugated quadratures of fields being jointlyacquired quantities.

[0125] One advantage is a reduced sensitivity the effects of an overlayerror of a spot in or on the substrate that is being imaged and aconjugate image of a pixel of a conjugate set of pixels of a multi-pixeldetector during the acquisition of the four electrical interferencesignal values of each spot in and/or on a substrate imaged usinginterferometric confocal microscopy. Overlay errors are errors in theset of four conjugate images of a respective set of conjugate detectorpixels relative to the spot being imaged.

[0126] Another advantage is that when operating in the scanning modethere is reduced sensitivity to effects of pulse-to-pulse variations ofa respective conjugate set of pulses of the input beam 24 to theinterferometer system.

[0127] Another advantage is that when operating in the scanning modethere is an increase in throughput since only one pulse of the source isrequired to generate the at least four electrical interference values.

[0128] A first embodiment comprises the interferometer system of FIGS.1a-1 c with interferometer 10 of the first embodiment shownschematically in FIG. 2a. Interferometer 10 comprises an interferometersuch as described in commonly owned U.S. Provisional Patent ApplicationNo. 60/447,254 (ZI-40) entitled “Transverse Differential InterferometricConfocal Microscopy” and U.S Patent Application filed Feb. 13, 2004(ZI-40) also entitled “Transverse Differential Interferometric ConfocalMicroscopy” both of which are by Henry A. Hill. The contents of the U.S.Provisional Patent Application and the U.S. Patent Application areherein incorporated in their entirety by reference.

[0129] Interferometer 10 of the first embodiment comprises a firstimaging system generally indicated as numeral 110, pinhole arraybeam-splitter 112, detector 70, and a second imaging system generallyindicated as numeral 210. The second imaging system 210 is low powermicroscope having a large working distance, e.g. Nikon ELWD and SLWDobjectives and Olympus LWD, ULWD, and ELWD objectives. The first imagingsystem 110 comprises an interferometric confocal microscopy systemdescribed in part in commonly owned U.S. Provisional Application No.60/442,982 [ZI-45] entitled “Interferometric Confocal MicroscopyIncorporating Pinhole Array Beam-Splitter” and U.S. patent applicationSer. No. ______ filed Jan. 27, 2004 (ZI-45) and also entitled“Interferometric Confocal Microscopy Incorporating Pinhole ArrayBeam-Splitter” both of which are by Henry A. Hill. The contents of bothof the U.S. Provisional Patent Application and the U.S. PatentApplication are herein incorporated in their entirety by reference.

[0130] First imaging system 110 is shown schematically in FIG. 2b. Theimaging system 110 is a catadioptric system such as described incommonly owned U.S. Pat. No. 6,552,852 B2 (ZI-38) entitled “Catoptricand Catadioptric Imaging System” and commonly owned U.S. patentapplication Ser. No. 10/366,651 (ZI-43) entitled “Catoptric AndCatadioptric Imaging Systems” wherein both of the patent applicationsare by Henry A. Hill, the contents of the two cited patent applicationsincorporated herein in their entirety by reference.

[0131] Catadioptric imaging system 110 comprises catadioptric elements140 and 144, beam-splitter 148, and convex lens 150. Surfaces 142B and146B are concave spherical surfaces with nominally the same radii ofcurvature and the conjugate points with respect to beam-splitter 148 ofrespective centers of curvature of surfaces 142B and 146B are the same.Surfaces 142A and 146A are convex spherical surfaces with nominally thesame radii of curvature. The centers of curvature of surfaces 142A and146A are transversely shifted in a plane parallel to the plane ofbeam-splitter 148 by a small radial displacements Δr₁ and Δr₂,respectively, and longitudinal displacements Δz₁ and Δz₂, respectivelywith respect to the centers of curvature of surfaces 146B and 142B,respectively. The relative orientation of the displacement vectorscorresponding to Δr₁ and Δr₂ is chosen to minimize the affects ofspurious beams as subsequently described. The relative displacements Δz₁and Δz₂ are selected to optimize the performance of interferometer 10with respect to acquisition of information about the surface ofsubstrate 60.

[0132] As a result of the small displacements just mentioned, theconjugate of the center of curvature of surface 142A, as seen throughbeam splitter 148, does not coincide with the center of curvature ofsurface 146A. (Or, equivalently, the conjugate of the center ofcurvature of surface 146A, as seen through beam splitter 148, does notcoincide with the center of curvature of surface 142A.) Rather, thosetwo points are displaced by an amount determined by the smalldisplacement of the two surfaces 142A and 146A relative to each other.And the vector of that displacement has a component that is normal tothe plane of beam splitter 148 and a component that is parallel to theplane oof beam splitter 148. Stated a different way, the line connectingthe centers of curvature of the two surfaces 142A and 146A is not normalto the plane of beam splitter 148 but rather it diverges from the normalby a small angle that is determined by the relative displacement of thetwo surfaces.

[0133] The center of curvature of convex lens 150 is the same as thecenter of curvature of surfaces 142B. The radius of curvature of surface146B is selected so as to minimize the loss in usable solid angle of theimaging system 110 and to produce a working distance for imaging system110 acceptable for an end use application, e.g., of the order of a mm.The radius of curvature of convex lens 150 is selected so that off-axisaberrations of the catadioptric imaging system 110 are compensated. Themedium of elements 140 and 144 may be for example CaF₂, fused silica orcommercially available glass such as SF11. The medium of convex lens 150may be for example CaF₂, fused silica, YAG, or commercially availableglass such as SF11. An important consideration in the selection of themedia of elements 140 and 144 and convex lens 150 will the transmissionproperties for the frequencies of beam 24.

[0134] Convex lens 152 has a center of curvature the same as the centerof curvature of convex lens 150. Convex lenses 150 and 152 are bondedtogether with pinhole beam-splitter 112 in between. Pinhole arraybeam-splitter 112 is shown in FIG. 2c. The pattern of pinholes inpinhole array beam-splitter is chosen to match the requirements of anend use application. An example of a pattern is a two dimensional arrayof equally spaced pinholes in two orthogonal directions. The pinholesmay comprise circular apertures, rectangular apertures, or combinationsthereof such as described in commonly owned U.S. patent application Ser.No. 09/917,402 (ZI-15) entitled “Multiple-Source Arrays for Confocal andNear-field Microscopy” by Henry A. Hill and Kyle Ferrio of which thecontents thereof are incorporated herein in their entirety by reference.The spacing between pinholes of pinhole array beam-splitter 112 is shownin FIG. 2c as b with aperture size a.

[0135] Input beam 24 is reflected by mirror 54 to pinhole beam-splitter112 where a first portion thereof is transmitted as reference beamcomponents of output beam components 130A and 130B (see FIG. 2a) and asecond portion thereof scattered as measurement beam components of beamcomponents 126A and 126B. The measurement beam components of beamcomponents 126A and 126B are imaged as measurement beam components ofbeam components 128A and 128B to an array of image spots in image planesdisplaced from the surface of substrate 60.

[0136] The arrays of image spots in the image planes displaced from thesurface of substrate 60 comprises a first and second array of imagespots with the second array of image spots transversely andlongitudinally displaced with respect to the first array of image spots.A corresponding pair of spots 164 and 166 of the first and second arraysof image spots are shown diagrammatically in FIGS. 2d and 2 e for thecase where the displacements of convex surfaces 142A and 146A lie in thex-z plane of FIGS. 2d and 2 e and (−2x₁,0,2z₁) and (−2x₂,0,−2z₂) are therespective locations of the pair of image spots. The displacements ofsurfaces 142A and 146A are restricted to the x-z plane in order tosimplify the description of the important aspects without limiting thescope or the spirit of the invention. The displacement of center ofcurvature of surface 142A is in the negative x direction and positive zdirection. The displacement of center of curvature of surface 146A is inthe positive x direction and negative z direction. The displacements ofthe pair of image spots 164 and 166 are a consequence of thedisplacements of centers of curvature of surfaces 142A and 146A. Anexample of a path of a beam contributing to image spot 164 is beam 126Eand an example of a path of a beam contributing to image spot 166 isbeam 126F (see FIG. 2d). Note that in FIG. 2d, the left side of thecatadioptric element illustrates how the reflected measurement beam(i.e., reflected off of beam splitter 148) is focused onto spot 164 andthe right side of the catadioptric element illustrates how thetransmitted measurement beam is focused onto spot 166. There is also areflected measurement beam on the right side which, like the reflectedmeasurement beam on the left side, is focused onto spot 164. Similarly,there is a transmitted measurement beam on the left side, which, likethe transmitted measurement beam on the right side, is focused onto spot166.

[0137] A portion of beam 126E is also reflected twice by beam-splitter148 and once by convex surface 142A to form an image spot 184 (see FIG.2d) at location (−2x₁/n,0,−2z₁/n) where n is the index of refraction ofconvex lenses 150 and 152. In addition, a portion of beam 126F istransmitted twice by beam-splitter 148 and reflected once by convexsurface 146A to form an image spot 186 (see FIG. 2d) at location(2x₂/n,0,2z₂/n).

[0138] Next consider the affects of catadioptric imaging system 110 onthe portions of the beams comprising image spots 164 and 166 that arereflected by the surface of substrate 60. The reflected image spots arerepresented by image sources 1641 and 166I as shown in the figure. Thereflected portions are part of the return measurement beam components ofbeams 128A and 128B and imaged by catadioptric imaging system 110 tofour spots 190, 192, 194, and 196 in the space of pinhole arraybeam-splitter 112 (see FIG. 2e). The locations of the respective spotswith respect to the pinhole source of beams 126E and 126F are (0,0,[2h₁−4z₁]/2), (0,0, [2h₂+4z₁]/2), (−2[x₁+x₂]/n,0,2h₂/n), and(2[x₁+x₂]/n,0,2h₁/n) where h₁ and h₂ are the heights of image spots 164and 166, respectively, below the surface of substrate 60. The surface ofsubstrate 60 is not indicated in FIG. 2e. The intersection of thevertical and horizontal dot-dash-dot lines located between image spots164 and 166 in FIG. 2e corresponds to center of curvature of concavesurface 146B (see FIG. 2b).

[0139] Portions of the beams forming image spot 190 and 192 aretransmitted by the pinhole corresponding to pinhole source of beams 126Eand 126F as a component of beam components 130A and 130B. The beamsforming image spots 184, 186, 194, and 196 are not transmitted by thepinhole corresponding to the pinhole source of beams 126E and 126F as aproperty of confocal imaging system 110. To further reduce the effectsof spurious beams generated by reflection of portions of the beamsforming image spots 184, 186, 194, and 196 by pinhole array 112, therespective surface of pinhole array 112 is coated with ananti-reflective coating.

[0140] The effects of spurious beams generated by reflection of portionsof the beams forming image spots 184, 186, 194, and 196 by pinhole array112 are reduced when the displacements in the x-y plane of the centersof curvature of convex surfaces 142A and 146A are selected to beorthogonal, e.g., the displacements of the centers of convex surfaces142A and 146A are in the x-z and y-z planes, respectively. Thecorresponding displacements are Δx₁ and Δy₂. The resulting locations ofimage spots 184, 186, 194, and 196 in x-y plane are shown schematicallyin FIG. 2f. With the image spot pattern shown in FIG. 2f, only thereflection by the low reflectivity surface of pinhole array 112 of beamsforming image spots 194 and 196 will generate secondary spurious beamswherein portions thereof can be subsequently transmitted by the pinholecorresponding to the pinhole source of beams 126E and 126F. Theamplitudes of the effects of the secondary spurious beams will be lessthan or of the order of 2% of the amplitudes of the portions of thebeams forming spots 190 and 192 transmitted by the corresponding pinholein pinhole array 112. For the resulting locations of image spots 184,186, 192, 194, and 196 shown schematically in FIG. 2c, the amplitudes ofthe effects of the corresponding spurious beams will be less than or ofthe order of 40% of the amplitude of the portions of the beams formingspots 190 and 192 transmitted by the corresponding pinhole in pinholearray 112.

[0141] The description of the affects of catadioptric imaging system 110on portions of the beams comprising image spots 164 and 166 that arescattered by sub-wavelength artifacts and/or defects on the surface ofsubstrate 60 is based on an analysis that is a variant of the analysisforming the basis of the description given of the affects ofcatadioptric imaging system 110 on the portions of the beams comprisingimage spots 164 and 166 that are reflected by the surface of substrate60.

[0142] The next step is the imaging of output beam components 130A and130B by imaging system 210 to an array of spots that coincide with thepixels of a multi-pixel detector 70 such as a CCD to generate an arrayof electrical interference signals 72. The array of electricalinterference signals is transmitted to signal processor and controller80 for subsequent processing for an array of conjugated quadratures.

[0143] The description of input beam 24 is the same as correspondingportions of the description given for input beam 24 of FIG. 1a withbeam-conditioner 22 configured as a two-frequency generator andfrequency-shifter shown in FIG. 1c. Input beam 24 comprises twocomponents that have different frequencies and have the same state ofplane polarization. The frequency of each component of input beam 24 isshifted between different frequency values by beam-conditioner 22according to control signal 74 generated by electronic processor andcontroller 80. Beam 20 comprises a single frequency component.

[0144] The conjugated quadratures of fields of the return measurementbeams are obtained using the bi-homodyne detection method wherein setsof four measurements of the electrical interference signals 72 are made.An array of conjugated quadratures of fields is measuredinterferometrically by interferometer confocal imaging system 10 whereineach conjugated quadratures comprises a difference of conjugatedquadratures of fields of beams scattered/reflected from a pair of spotsin or on a substrate. The array of conjugated quadratures is measuredjointly, i.e., simultaneously, and the components of each conjugatedquadratures are measured jointly.

[0145] The relative phases of the beams subsequently scattered/reflectedby the pair of spots in or on a substrate are adjusted by the control ofa single interferometer system parameter, the relative optical pathlengths of measurement and return measurement beam components respectivespots of the pairs of spots in or on substrate 60. The relative phasesare adjusted by making a longitudinal displacement of convex surface142A with respect to convex surface 146A. This may be achieved bychanging the thickness of element 140 relative to the thickness ofelement 144. Alternatively, a thin layer may be added to surface 142Aand/or surface 146A. Another example of a technique to introduce achange in relative phase is to add a concave reflecting surface next toconvex surface 142A with an air gap such that the air gap thickness maybe adjusted. In the latter example, the convex surface 142A would beanti-reflective coated.

[0146] The measured conjugate quadratures in the first embodiment areproportional to components of complex amplitude V₂ (h₁,z₁,h₂, z₂,χ) canto a good approximation be written as $\begin{matrix}\begin{matrix}{{V_{2}\left( {h_{1},z_{1},h_{2},z_{2},\chi} \right)} = {{R_{1}^{1/2}{j_{0}\left( {\alpha \left( {h_{1} - {2z_{1}}} \right)} \right\rbrack}^{{- }\quad {\beta {({h_{1} - {2z_{1}}})}}}} +}} \\{{^{\quad \chi}R_{2}^{1/2}{j_{0}\left\lbrack {\alpha \left( {h_{2} + {2z_{2}}} \right)} \right\rbrack}^{{- }\quad {\beta {({h_{2} + {2z_{2}}})}}}}}\end{matrix} & (29)\end{matrix}$

[0147] where R₁ ^(1/2) and R₂ ^(1/2) are the complex reflectivitycoefficients of the surface of substrate 60 for the fields of the beamsforming spots 190 and 192, respectively,

α=2k(1−cos θ₀),  (30)

β=2k(1+cos θ₀),  (31)

[0148] j_(p) (x) is the spherical Bessel function of order p=0,1, 2, . .. , sin θ₀ is the numerical aperture of the imaging system in the imagespace of substrate 60, and χ is the relative phase of the components ofbeams forming spots 190 and 192 at a corresponding pinhole of pinholearray beam-splitter 112. Descriptions of derivations that form the basisfor the two terms in Equation (29) may be found in references such asthe book edited by T. Wilson, Confocal Microscopy, Academic Press(1990), the contents of which are herein incorporated in their entiretyby reference.

[0149] The coefficient exp(iχ) in Equation (29) is written as acoefficient with a magnitude of 1 to a good approximation: the pinholesources for each of the beams forming spots 164 and 166 (see FIG. 2d)are the same pinhole of pinhole array beam-splitter 112, the pinholesperforming the confocal spatial filtering of the beams forming spots 190and 192 are the same pinhole of pinhole array beam-splitter 112 (seeFIGS. 2c and 2 e), and the portions of the beams forming spots 190 and192 subsequently spatially filtered, i.e., transmitted, by the samepinhole are detected by the same pixel of detector 70. This featurerepresents one of the distinguishing advantages of the imaging system110.

[0150] The second embodiment comprises the first embodiment configuredfor operation in a dark field mode. In the dark field configuration ofthe second embodiment,

χ=π.  (32)

[0151] and Equation (29) assumes the form $\begin{matrix}\begin{matrix}{{V_{2}\left( {h_{1},z_{1},h_{2},z_{2},{\chi = \pi}} \right)} = {{R_{1}^{1/2}{j_{0}\left( {\alpha \left( {h_{1} - {2z_{1}}} \right)} \right\rbrack}^{{- }\quad {\beta {({h_{1} - {2z_{1}}})}}}} -}} \\{{R_{2}^{1/2}{j_{0}\left\lbrack {\alpha \left( {h_{2} + {2z_{2}}} \right)} \right\rbrack}{^{{- }\quad {\beta {({h_{2} + {2z_{2}}})}}}.}}}\end{matrix} & (33)\end{matrix}$

[0152] The remainder of the description of the properties of themeasured conjugated quadratures will be with respect to Equation (33)and the second embodiment. The extension of the description to adescription of the measured conjugated quadratures of the firstembodiment and Equation (29) will be apparent to one skilled in the art.

[0153] Properties of Equation (33) are easily recognized by examinationof low order terms of h₁ and h₂ in a power series representation, i.e.,$\begin{matrix}\begin{matrix}{{V_{2}\left( {h_{1},z_{1},h_{2},z_{2},{\chi = \pi}} \right)} = \left\lbrack {{R_{1}^{1/2}{j_{0}\left( {{- 2}\alpha \quad z_{1}} \right)}^{\quad 2\quad \beta \quad z_{1}}} -} \right.} \\{\left. {R_{2}^{1/2}{j_{0}\left( {2\alpha \quad z_{2}} \right)}^{{- }\quad 2\quad \beta \quad z_{2}}} \right\rbrack -} \\{{\alpha\left\lbrack {{R_{1}^{1/2}{j_{1}\left( {{- 2}\alpha \quad z_{1}} \right)}^{\quad 2\quad \beta \quad z_{1}}h_{1}} -} \right.}} \\{\left. {R_{2}^{1/2}{j_{1}\left( {2\alpha \quad z_{2}} \right)}^{{- }\quad 2\quad \beta \quad z_{2}}h_{2}} \right\rbrack -} \\{{\quad {\beta\left\lbrack {{R_{1}^{1/2}{j_{0}\left( {{- 2}\alpha \quad z_{1}} \right)}^{\quad 2\quad \beta \quad z_{1}}h_{1}} -} \right.}}} \\{\left. {R_{2}^{1/2}{j_{0}\left( {2\alpha \quad z_{2}} \right)}^{{- }\quad 2\quad \beta \quad z_{2}}h_{2}} \right\rbrack.}\end{matrix} & (34)\end{matrix}$

[0154] For the non-limiting assumption z₁=z₂, Equation (34) simplifiesto the expression $\begin{matrix}\begin{matrix}{{V_{2}\left( {h_{1},z_{1},h_{2},z_{2},{\chi = \pi}} \right)} = {{j_{0}\left( {2\quad \alpha \quad z_{1}} \right)}\left\lbrack {{R_{1}^{1/2}^{\quad 2\quad \beta \quad z_{1}}} -} \right.}} \\{\left. {R_{2}^{1/2}^{{- }\quad 2\quad \beta \quad z_{2}}} \right\rbrack +} \\{{\alpha \quad {{j_{1}\left( {2\quad \alpha \quad z_{1}} \right)}\left\lbrack {{R_{1}^{1/2}^{\quad 2\quad \beta \quad z_{1}}h_{1}} +} \right.}}} \\{\left. {R_{2}^{1/2}^{{- }\quad 2\quad \beta \quad z_{2}}h_{2}} \right\rbrack -} \\{{\quad \beta \quad {{j_{0}\left( {2\quad \alpha \quad z_{1}} \right)}\left\lbrack {{R_{1}^{1/2}^{\quad 2\quad \beta \quad z_{1}}h_{1}} -} \right.}}} \\{\left. {R_{2}^{1/2}^{{- }\quad 2\quad \beta \quad z_{2}}h_{2}} \right\rbrack.}\end{matrix} & (35)\end{matrix}$

[0155] By combining terms of h₁ and h₂, Equation (35) reduces to$\begin{matrix}\begin{matrix}{{V_{2}\left( {h_{1},z_{1},h_{2},z_{2},{\chi = \pi}} \right)} = {{{j_{0}\left( {2\quad \alpha \quad z_{1}} \right)}\left\lbrack {{R_{1}^{1/2}^{\quad 2\quad \beta \quad z_{1}}} - {R_{2}^{1/2}^{{- }\quad 2\quad \beta \quad z_{2}}}} \right\rbrack} +}} \\{{R_{1}^{1/2}{^{\quad 2\quad \beta \quad z_{1}}\left\lbrack {{\alpha \quad {j_{1}\left( {2\quad \alpha \quad z_{1}} \right)}} - {\quad \beta \quad {j_{0}\left( {2\quad \alpha \quad z_{1}} \right)}}} \right\rbrack}h_{1}} +} \\{R_{2}^{1/2}{^{{- }\quad 2\quad \beta \quad z_{1}}\left\lbrack {{\alpha \quad {j_{1}\left( {2\quad \alpha \quad z_{1}} \right)}} + {\quad \beta \quad {j_{0}\left( {2\quad \alpha \quad z_{1}} \right)}}} \right\rbrack}{h_{2}.}}\end{matrix} & (36)\end{matrix}$

[0156] Another useful form of Equation (35) is obtained by writing it interms of (h₁+h₂)/2 and (h₁−h₂)/2. $\begin{matrix}\begin{matrix}{{V_{2}\left( {h_{1},z_{1},h_{2},z_{2},{\chi = \pi}} \right)} = {{{j_{0}\left( {2\quad \alpha \quad z_{1}} \right)}\left\lbrack {{R_{1}^{1/2}^{\quad 2\quad \beta \quad z_{1}}} - {R_{2}^{1/2}^{{- }\quad 2\quad \beta \quad z_{1}}}} \right\rbrack} +}} \\{{\begin{Bmatrix}{{\alpha \quad {j_{1}\left( {2\quad \alpha \quad z_{1}} \right)}\left( {{R_{1}^{1/2}^{\quad 2\quad \beta \quad z_{1}}} + {R_{2}^{1/2}^{{- }\quad 2\quad \beta \quad z_{1}}}} \right)} -} \\{\quad \beta \quad {j_{0}\left( {2\quad \alpha \quad z_{1}} \right)}\left( {{R_{1}^{1/2}^{\quad 2\quad \beta \quad z_{1}}} - {R_{2}^{1/2}^{{- }\quad 2\quad \beta \quad z_{1}}}} \right)}\end{Bmatrix}\left( \frac{h_{1} + h_{2}}{2} \right)} +} \\{\frac{1}{2}\begin{Bmatrix}{{\alpha \quad {j_{1}\left( {2\quad \alpha \quad z_{1}} \right)}\left( {{R_{1}^{1/2}^{\quad 2\quad \beta \quad z_{1}}} - {R_{2}^{1/2}^{{- }\quad 2\quad \beta \quad z_{1}}}} \right)} -} \\{\quad \beta \quad {j_{0}\left( {2\quad \alpha \quad z_{1}} \right)}\left( {{R_{1}^{1/2}^{\quad 2\quad \beta \quad z_{1}}} + {R_{2}^{1/2}^{{- }\quad 2\quad \beta \quad z_{1}}}} \right)}\end{Bmatrix}{\left( {h_{1} - h_{2}} \right).}}\end{matrix} & (37)\end{matrix}$

[0157] One important application of the second embodiment is thedetermination of differences in height of a first region comprising afeature or an artifact relative to a neighboring second region used as areference region. The first and second regions would have heightscorresponding to h₁ and h₂, respectively. The factors (h₁+h₂)/2 and(h₁−h₂) represent the average height and the difference in heights ofthe two regions on the surface of substrate 60 corresponding to beamsforming spots 190 and 192. The coefficients of h₁ and h₂ in Equation(36) and coefficients of (h₁+h₂)/2 and (h₁−h₂) in Equation (37) can beindependently measured by measuring V₂ (h₁,z₁, h₂, z₂,χ=π) withsubstrate 60 stationary in the x-y plane and with transducers 86A and86B introducing a scan in z to obtain measurements at at least twodifferent positions (thereby changing h₁ and h₂ and causing the average(h₁+h₂)/2 to change but keeping the difference (h₁−h₂) the same) andscans in orientation of substrate 60 for known values of R₁ ^(1/2) andR₂ ^(1/2) (wherein the scans are achieved by rotating the substrate toobtain at least two measurements in which the average (h₁+h₂)/2 does notchange but the slope (h₁−h₂) does). The properties of the region used asa reference with respect to height are determined by a more globalexamination of the surface of substrate 60.

[0158] An error in the either of the values assumed for reflectivitycoefficients R₁ ^(1/2) and R₂ ^(1/2) can introduce an error in thedetermination of (h₁−h₂). Information about local values of reflectivitycoefficients R₁ ^(1/2) and R₂ ^(1/2) can be obtained by an independentmeasurement. The measured conjugate quadratures in the second embodimentof cited U.S. Provisional Application No. 60/447,254 (ZI-40) U.S. patentapplication Ser. No. ______ filed Feb. , 2004 (ZI-40) entitled“Transverse Differential Interferometric Confocal Microscopy” areproportional to components of complex amplitude V₁ (h₁,0,h₁ ,0,χ=π). Thecomplex amplitude V ₁ (h₁,0,h₁,0, χ=π) of the cited U.S. ProvisionalApplication No. 60/447,254 (ZI-40) U.S. patent application Ser. No.______ filed Feb. , 2004 (ZI-40) entitled “Transverse DifferentialInterferometric Confocal Microscopy” corresponds to a special case ofEquation (36), i.e.,

V ₁(h ₁,0,h ₂,0,χ=π)=[R ₁ ^(1/2) −R ₂ ^(1/2)](1−iβh ₁).  (38)

[0159] Thus an independent determination the difference in local valuesof reflectivity coefficients R₁ ^(1/2) and R₂ ^(1/2) can be obtainedfrom a measured value of complex amplitude V₁ (h₁,0, h₁,0, χ=A) and usedto reduce an error in the determination of (h₁−h₂).

[0160] The measurement of differences in reflectivity coefficients canbe also used to obtain information about properties of the respectiveregions of substrate 60 such as information about the complex index ofrefraction of one the regions relative to the complex index ofrefraction of a second of the regions.

[0161] The selection of values for z₁ in the second embodiment is madeto optimize the sensitivity of V₂ (h₁,z₁,h₂,z₂,χ=π) such as expressed byEquations (36) and (37) to quantities for which information is desiredin a given end use application. In the selection process, properties ofthe spherical Bessel functions will also play an important role. Oneproperty of j₁ (x) is that j₁ (x) exhibits a maximum for x₁≅2.1 andanother property is that j₀ (x)=0 for x≅3.15.

[0162] Operation in a dark field mode leads to both reduced systematicand statistical errors in the information represented by the arrays ofconjugated quadratures and increased throughput. The information maycomprise the transverse derivative of a profile of one or more surfacesof substrate 60 in or on substrate 60; one-dimensional, two-dimensional,and three-dimensional transverse differential images of substrate 60;critical dimensions of features or artifacts on or in substrate 60, andthe sizes and locations of sub-wavelength defects in or on substrate 60.

[0163] The background components of return measurement beams generatedby scattering/reflection of measurement beam components by conjugatespots are the same and therefore do not contribute to the electricalinterference signals 72. Accordingly, the background components do notcontribute to either the average values of the electrical interferencesignals 72 or to interference terms in electrical interference signals72 for both the first and second embodiments.

[0164] The reduction of statistical error is also a direct consequenceof operation in the dark field mode. The contributions of backgroundfields are removed/eliminated in the second embodiment by thesuperposition of background fields arranged to have the same amplitudesand phase differences of π and not by the subtraction of intensities. Asa result of the dark field, the intensity of beam 24 can be increasedsignificantly without saturation of detector 70 and a correspondingreduction in statistical error is achieved.

[0165] The increase in throughput is a direct consequence of operatingin a dark field mode. The time required to achieve a certain precisionin the measured array of conjugated quadratures is reduced by anincrease of the intensity of beam 24 that is permitted by operating inthe dark field mode. As a result of the dark field, the intensity ofbeam 24 can be increased significantly without saturation of detector70.

[0166] Also when operating in a dark field mode, a measured conjugatedquadratures of fields corresponding to a pair of spots comprising asub-wavelength artifact in a locally isotropic section of substrate 60represents information about the sub-wavelength artifact relative to areference sub-wavelength artifact. The reference sub-wavelength artifacthas properties of the locally isotropic section and dimensions similarto those of the artifact. Accordingly, properties measured includeinformation about critical dimensions and location of the sub-wavelengthartifact in or on substrate 60.

[0167] Also when operating in a dark field mode, a measured conjugatedquadratures of fields corresponding to a pair of spots comprising asub-wavelength defect in a locally isotropic section of substrate 60represents information about the sub-wavelength defect relative to areference sub-wavelength defect. The reference sub-wavelength defect hasproperties of the locally isotropic section and dimensions similar tothose of the defect. Accordingly, properties measured includeinformation about dimensions and location of the sub-wavelength defectin or on substrate 60.

[0168] The accuracy of the interferometric compensation of backgroundfields is high in the first and second embodiments for several reasons.The high accuracy of interferometric compensation is not dependent onthe properties of pinholes in pinhole array beam-splitter 112, e.g., thediameter of a pinhole could change by a factor of 2 for example and/orthe shape of a pinhole could change from a round aperture to a squareaperture and the level of interferometric compensation for associatedbackground fields would not change. The amplitudes and phases ofbackground fields associated with a first spot of a pair of spots arethe same as the amplitudes and phases of background fields associatedwith a second spot of a pair of spots independent of properties ofpinholes in pinhole array beam-splitter 112.

[0169] Compensation for the effects of a mismatch of indices ofrefraction at the interface of substrate 60 with an external a medium,e.g., air, may be compensated in the first and second embodiments by theaddition of a thin low index of refraction layer between pinhole arraybeam-splitter 112 and lens 150 such as described in U.S. ProvisionalPatent Application No. 60/444,707(ZI-44) entitled “Compensation forEffects of Mismatch in Indices of Refraction at a Substrate-MediumInterface in Confocal and Interferometric Confocal Microscopy” and U.S.patent application Ser. No. ______ filed Feb. 4, 2004 (ZI-44) and alsoentitled “Compensation for Effects of Mismatch in Indices of Refractionat a Substrate-Medium Interface in Confocal and Interferometric ConfocalMicroscopy” both of which are by Henry A. Hill. The contents of the U.S.Provisional Patent Application and the U.S. Patent Application areincorporated herein in their entirety by reference. With thecompensation for effects of the mismatch in refractive indices, aninterior portion of a substrate is imaged with a lateral resolution downto of the order of 100 nm and a longitudinal resolution down to of theorder of 200 nm. The images of the interior portion are obtained with aworking distance of the order of a mm and for depths within thesubstrate of the order of at least 3 microns.

[0170] The throughputs of the first and second embodiments can befurther increased by the use of a pinhole array beam-splitter that iscoupled to input beam 24 by a guided wave structure such as described incommonly owned U.S. Provisional Patent Application No. 60/445,739(ZI-39) entitled “Multiple-Source Arrays Fed By Guided Wave StructuresAnd Resonant Structures For Confocal And Near-Field Confocal Microscopy”and U.S. patent application Ser. No. ______ filed Feb. 6, 2004 (ZI-39)and also entitled “Multiple-Source Arrays Fed By Guided Wave StructuresAnd Resonant Structures For Confocal And Near-Field Confocal Microscopy”both of which are by Henry A. Hill. The contents of the cited U.S.Provisional Patent Application and the U.S. Patent Application areincorporated herein in their entirety by reference.

[0171] The first and second embodiments may also be configured forquad-homodyne detection such as described herein and in cited U.S.Provisional Patent Application No. 60/442,858 (ZI-47) and cited U.S.Patent Application filed Jan. 27, 2004 (ZI-47) entitled “Apparatus andMethod for Joint Measurements of Conjugated Quadratures of Fields ofReflected/Scattered Beams by an Object in Interferometry” (ZI-47).

[0172] A third embodiment is shown schematically in FIG. 3. The thirdembodiment can be configured to be functionally equivalent to the firstand second embodiments. The primary difference between the first andsecond embodiments and the third embodiment is replacement of thepinhole array beam-splitter 112 with traditional confocal pinhole arrays112A, 112B, and 112C.

[0173] Referring to FIG. 3, input beam 24 is incident on polarizingbeam-splitter 330 and a first portion thereof is transmitted as ameasurement beam of interferometer 410 and a second portion thereof isreflected as a reference beam of interferometer 410 after reflection bymirrors 332 and 334. The measurement beam and the reference beam areincident on pinhole arrays 112A and 112B, respectively. Pinhole arrays112A and 112B are each conjugates of pinhole array 112C.

[0174] A portion of the reference beam incident on pinhole array 112B istransmitted by beam-splitter 340 and a portion thereof focused by lens360 to an array of spots on pinhole array 112C.

[0175] A portion of the measurement beam incident on pinhole array 112Ais transmitted by beam-splitter 340 and first and second portionsthereof are focused to arrays of spots on substrate 60. The firstportion is focused to a first array of spots after a reflection andtransmission by polarizing beam-splitter 342, a double pass throughquarter-wave plate 346, reflected by concave mirror 350, and focused bylens 354. The second portion is focused to a second array of spots aftera transmission and reflection by polarizing beam-splitter 342, a doublepass through quarter-wave plate 348, reflected by convex mirror 352, andfocused by lens 354. The description the first and second arrays ofspots is the same as description of the corresponding arrays of spots ofthe first and second embodiments. The relative transverse andlongitudinal shifting the first and second arrays of spots is controlledby rotations and longitudinal displacements of concave mirror 350relative to convex mirror 352. The orientation of optical system 310which in practice is at an angle of 45 degrees to the plane of FIG. 3 ishowever shown as oriented in the plane in FIG. 3 in order to simplifythe description without limiting the scope or spirit of the presentinvention.

[0176] Portions of the measurement beams that form the first and secondarrays of spots are reflected/scattered by substrate 60 as first andsecond arrays of return measurement beam components, respectively. Thefirst array of return measurement beam components retraces the path ofits progenitor array of measurement beam components through imagingsystem 310 and a portion thereof is focused to an array of spots atpinhole array 112C after reflection by beam-splitter 340. The secondarray of return measurement beam components retraces the path of itsprogenitor array of measurement beam components through imaging system310 and a portion thereof is focused to an array of spots at pinholearray 112C after reflection by beam-splitter 340.

[0177] The description of the two arrays of spots at pinhole array 112Cis the same as portion of the description given for the correspondingarrays of spots in the first and second embodiments at pinhole arraybeam-splitter 112 except that the displacements of the spots are notreduced by the factor 1/n. The index of refraction of the mediumcontiguous to pinhole array 112C is assumed to be 1 although it could beotherwise without departing from the scope and the spirit of the presentinvention.

[0178] Portions of the superimposed array of spots and of the referencebeam are transmitted by pinhole array 112C and detected by detector 70after transmission by analyzer 362 to generate electrical interferencesignal 72. Analyzer 362 mixes the polarization states of the transmittedportions of the superimposed array of spots and of the reference beam.

[0179] The description of input beam 24 is the same as correspondingportions of the description given for input beam 24 of FIG. 1a withbeam-conditioner 22 configured as a two-frequency generator andphase-shifter shown in FIG. 1b and beam 20 comprising a single frequencycomponent. Input beam 24 comprises two components that have differentfrequencies and each component has two components of different states ofplane polarization. The relative phases of the components of input beam24 are shifted between different values according to control signal 74generated by electronic processor and controller 80 as described in thediscussion of beam-conditioner 22.

[0180] The remaining portion of the description of the third embodimentis the same as corresponding portions given for the first and secondembodiments.

[0181] In some embodiments, pinhole array beam-splitter 112 may bescanned in a direction opposite to the direction of scan of substrate 60and with a speed such that the conjugate images of the pinholes ofpinhole array beam-splitter 12 stay superimposed with spots on or insubstrate 60 that are being imaged. This scanning mode of operation isanalogous to the relative motions of reticle stage and a wafer stage ofa lithography tool operating in a scanning mode. The issue oftraditional critical alignment of conjugate confocal pinholes in aconfocal microscopy system is nonexsistent, i.e. the registration of thepinholes generating the array of reference beams and the pinholesgenerating the array of measurement beams is automatic.

[0182] A fourth embodiment comprises the interferometer system of FIGS.1a-1 c with interferometer 10 comprising an interferometric far-fieldconfocal microscope such as described in cited U.S. Pat. No. 5,760,901.In the fourth embodiment, beam-conditioner 22 is configured as the twofrequency generator and phase-shifter shown in FIG. 1b. Embodiments incited U.S. Pat. No. 5,760,901 are configured to operate in either thereflection or transmission mode. The fourth embodiment has reducedeffects of background because of background reduction features of citedU.S. Pat. No. 5,760,901.

[0183] A fifth embodiment comprises the interferometer system of FIGS.1a-1 c with interferometer 10 comprising an interferometric far-fieldconfocal microscope such as described in cited U.S. Pat. No. 5,760,901wherein the phase masks are removed. In the fifth embodiment,beam-conditioner 22 is configured as the two frequency generator andphase-shifter shown in FIG. 1b. Embodiments in cited U.S. Pat. No.5,760,901 are configured to operate in either the reflection ortransmission mode. The fifth embodiment with the phase masks ofembodiments of cited U.S. Pat. No. 5,760,901 removed representapplications of confocal techniques in a basic form.

[0184] A sixth embodiment comprises the interferometer system of FIGS.1a-1 c with interferometer 10 comprising an interferometric far-fieldconfocal microscope such as described in cited U.S. Pat. No. 6,480,285B1. In the sixth embodiment, beam-conditioner 22 is configured as thetwo-frequency generator and phase-shifter shown in FIG. 1b. Embodimentsin cited U.S. Pat. No. 6,480,285 B1 are configured to operate in eitherthe reflection or transmission mode. The sixth embodiment has reducedeffects of background because of background reduction features of citedU.S. Pat. No. 6,480,285 B1.

[0185] A seventh embodiment comprises the interferometer system of FIGS.1a-1 c with interferometer 10 comprising an interferometric far-fieldconfocal microscope such as described in cited U.S. Pat. No. 6,480,285B1 wherein the phase masks are removed. In the fifth embodiment,beam-conditioner 22 is configured as the two-frequency generator andphase-shifter shown in FIG. 1b. Embodiments in cited U.S. Pat. No.6,480,285 B1 are configured to operate in either the reflection ortransmission mode. The seventh embodiment with the phase masks ofembodiments of cited U.S. Pat. No. 6,480,285 B1 removed representapplications of confocal techniques in a basic form.

[0186] An eighth embodiment comprises the interferometer system of FIGS.1a-1 c with interferometer 10 comprising an interferometric near-fieldconfocal microscope such as described in cited U.S. Pat. No. 6,445,453(ZI-14). In the eighth embodiment, beam-conditioner 22 is configured asthe two-frequency generator and phase-shifter shown in FIG. 1b.Embodiments in cited U.S. Pat. No. 6,445,453 are configured to operatein either the reflection or transmission mode. The eighth embodiment ofcited U.S. Pat. No. 6,445,453 in particular is configured to operate inthe transmission mode with the measurement beam separated from thereference beam and incident on the substrate being imaged by anon-confocal imaging system, i.e., the measurement beam at the substrateis not an image of an array of pinholes but an extended spot.Accordingly, the corresponding embodiments of the eighth embodimentrepresent an application of bi-homodyne detection method in anon-confocal configuration for the measurement beam.

[0187] Other embodiments may use the quad-homodyne detection methodinstead of the bi-homodyne detection method as variants of theembodiments. For the embodiments that are based on the apparatus shownin FIGS. 1a-1 c, the corresponding variants of the embodiments that usethe quad-homodyne detection method use variants of the apparatus shownin FIGS. 1a-1 c. In the variants of the apparatus such as used in thefirst embodiment, microscope 220 is modified to include a dispersiveelement such as a direct vision prism and/or a dichroic beam-splitter.When configured with a dichroic beam-splitter, a second detector isfurther added to the system. Descriptions of the variants of theapparatus are the same as corresponding portions of descriptions givenfor corresponding systems in cited U.S. Provisional Application No.60/442,982 (ZI-45) and U.S. Patent Application No. ______ filed Jan. 27,2004 (ZI-45) entitled “Interferometric Confocal Microscopy IncorporatingPinhole Array Beam-Splitter”.

[0188] Variants of embodiments may be configured to use thedouble-homodyne detection method for generation of non-jointmeasurements of conjugated quadratures. Input beam 24 of the variants ofthe embodiments comprise four frequency components and with the designof the dispersion of a direct vision prism and/or a dichroicbeam-splitter such as described with respect to embodiments that areconfigured to use the quad-homodyne detection method and the selectionof the four frequencies such that each of the four frequency componentsof beam 32 are directed to different pixels of detector 70. Four arraysof electrical interference signal values are obtained simultaneously andprocessed for amplitudes of conjugated quadratures using the proceduredescribed herein for the single-homodyne detection method.

What is claimed is:
 1. A differential interferometric confocalmicroscope for measuring an object, said microscope comprising: asource-side pinhole array; a detector-side pinhole array; and aninterferometer that images the array of pinholes of the source-sidepinhole array onto a first array of spots located in front of an objectplane located near where the object is positioned and onto a secondarray of spots behind the object plane, wherein the first and secondarrays of spots are displaced from each other in both a direction normalto the object plane and a direction parallel to the object plane, saidinterferometer also imaging the first arrays of spots onto a first imageplane that is behind the detector-side pinhole array and imaging thesecond array of spots onto a second image plane that is in front of thedetector-side pinhole array wherein each spot of the imaged first arrayof spots is aligned with a corresponding different spot of the imagedsecond array of spots and a corresponding different pinhole of thedetector-side pinhole array.
 2. A differential interferometric confocalmicroscope for measuring an object, said microscope comprising: asource-side pinhole array; a detector-side pinhole array; and aninterferometer that images each pinhole of the source-side pinhole arrayonto a corresponding different pair of two locations, one of which liesin a first object plane and the other of which lies in a second objectplane that is parallel to and displaced from the first object plane,thereby generating a first image of the source-side pinhole array in thefirst object plane and a second image of the source-side pinhole arrayin the second object plane, said interferometer also projecting a firstarray of return measurement beams from the first image and a secondarray of return measurement beams from the second image toward thedetector-side pinhole array to produce a first array of converging beamsand a second array of converging beams, wherein the detector-sidepinhole array generates an array of conjugated quadratures of fieldsthat is a difference of conjugated quadratures of fields of the firstand second arrays of converging beams.
 3. A differential interferometricconfocal microscope for measuring an object and which has, in thevicinity of where the object being measured is to be located, a firstobject plane and a second object plane that is displaced from andparallel to the first object plane, said microscope comprising: asource-side pinhole array; a detector-side pinhole array; and aninterferometer that receives a beam from a selected pinhole of thesource-side pinhole array and converges a first part of that receivedbeam onto a corresponding first location in the first object plane and asecond part of that received beam onto a corresponding second locationin the second object plane, said interferometer also arranged to receivea first return beam from the first location and a second return beamfrom the second location and converge at least a part of each of thefirst and second return beams onto a corresponding pinhole of thedetector-side pinhole array to produce a difference of conjugatedquadratures of fields of the first and second return beams converging onthat corresponding pinhole, wherein said selected pinhole is any pinholeof the source-side pinhole array.
 4. A differential interferometricconfocal microscope for measuring an object, said microscope comprising:a source-side pinhole array for producing an array of input beams; adetector-side pinhole array; and an interferometer including: a firstoptical element providing a first reflecting surface; a second opticalelement providing a second reflecting surface; and a beam splitterpositioned between the first and second optical elements, wherein thebeam splitter produces from the array of input beams a first array ofmeasurement beams and a second array of measurement beams, wherein thefirst reflecting surface participates in focusing the first array ofmeasurement beams onto a first array of locations on a first objectplane in object space and the second reflecting surface participates infocusing the second array of measurement beams onto a second array oflocations on a second object plane in object space, said first andsecond object planes being parallel to and displaced from each other,wherein the first array of measurement beams generates a first array ofreturn beams from the object and the second array of measurement beamsgenerates a second array of return beams from the object, wherein thefirst reflecting element participates in producing from the first arrayof return beams a first array of converging beams that converge to afirst array of spots on a first image plane and the second reflectingelement participates in producing from the second array of return beamsa second array of converging beams that converge onto a second array ofspots on a second image plane, said first and second image planes beingadjacent to and on opposite sides of the detector-side pinhole array,and wherein the detector-side pinhole array combines the first andsecond arrays of converging beams to form an array of output beams. 5.The differential interferometric confocal microscope of claim 4 whereina single pinhole array serves as both the source-side pinhole array andthe detector-side pinhole array.
 6. The differential interferometricconfocal microscope of claim 5, wherein the first optical element islocated between said single pinhole array and the beam splitter andwherein the second optical element is located between a location atwhich the object is positioned during use and the beam splitter, whereinthe first reflecting surface has a center of curvature for which thereis a corresponding conjugate as viewed through the beam splitter, andwherein the second reflecting surface has a center of curvature that isdisplaced relative to the corresponding conjugate of the center ofcurvature of the first reflecting surface.
 7. The differentialinterferometric confocal microscope of claim 6, wherein the conjugate ofthe center of curvature of the first reflecting surface and the centerof curvature of the second reflecting surface are displaced from eachother in a first direction that is normal to a plane defined by the beamsplitter and in a second direction that is parallel to the plane definedby the beam splitter.
 8. The differential interferometric confocalmicroscope of claim 7, wherein the first reflecting surface participatesin focusing the first array of measurement beams via the beam splitteronto the first array of locations and the second reflecting surfaceparticipates in focusing the second array of measurement beams via thebeam splitter onto the second array of locations.
 9. The differentialinterferometric confocal microscope of claim 8, wherein the firstreflecting element participates in combination with the beam splitter inproducing the first array of converging beams and the second reflectingelement participates in combination with the beam splitter in producingthe second array of converging beams.
 10. The differentialinterferometric confocal microscope of claim 9 wherein the firstreflecting surface is substantially concentric with a point on theobject.
 11. The differential interferometric confocal microscope ofclaim 9, wherein the second optical element provides a refractingsurface positioned between the object and the beam splitter to receivelight rays from the object.
 12. The differential interferometricconfocal microscope of claim 11, wherein the first reflecting surfacesubstantially conforms to a sphere having a first radius and therefracting surface conforms to a sphere having a second radius, whereinthe first radius is greater than the second radius.
 13. The differentialinterferometric confocal microscope of claim 9, wherein the firstoptical element provides a refracting surface positioned between thebeam splitter and said single pinhole array.
 14. The differentialinterferometric confocal microscope of claim 9 wherein the secondreflecting surface is substantially concentric with an image point onsaid single pinhole array.
 15. The differential interferometric confocalmicroscope of claim 13, wherein the second reflecting surfacesubstantially conforms to a sphere having a first radius and therefracting surface conforms to a sphere having a second radius, whereinthe first radius is greater than the second radius.
 16. The differentialinterferometric confocal microscope of claim 9, wherein said singlepinhole array is a two-dimensional array.
 17. The differentialinterferometric confocal microscope of claim 16, wherein thetwo-dimensional array is of equally-spaced holes.
 18. The differentialinterferometric confocal microscope of claim 17, wherein theequally-spaced holes are circular apertures.
 19. The differentialinterferometric confocal microscope of claim 9, wherein the first andsecond object planes are separated from each other on the order of thelongitudinal resolution of the differential confocal interferometricmicroscope.